In this work we contribute to the literature about the optimal asset allocation in continuous-time. In particular, we consider the problem of maximising the expected utility of the investor's final wealth over a finite time horizon. We develop a suitable framework in the dynamic stochastic optimal control theory in order to analyse the optimal asset allocation problem for an institutional investor like a bank, an insurance company, an investment fund, or a pension fund. Such an investor cannot control the contributions to and withdrawals from the managed wealth. In fact, while the classical consumption-portfolio problem considers consumption as a control variable, in our analysis the flows of wealth that are different from the coupons and dividends, are just state variables. We refer to them as "background variables". Furthermore, the analysis explicitly takes into account the inflation risk that is generally neglected by the asset allocation literature. In such a context we present some quasi-explicit solutions for the optimal asset allocation problem without specifying any particular functional form for the drift and diffusion terms of the stochastic differential equations describing the financial market, the background variables, and inflation. The institutional investor's attitude towards risk is supposed to be described by an increasing and concave utility function whose risk aversion is absolutely constant, relatively constant, or hyperbolic according to the problem setting that must be solved. Finally, we explicitly consider the case of a pension fund that must maximise the expected utility of its surplus. Unlike the analyses studying the problem of a non-actuarial institutional investor, the case of a pension fund requires the introduction of two new characteristics: (i) the different behaviour of the fund's wealth during the accumulation and the decumulation phases, and (ii) the mortality risk. We develop a set up aimed at finding out how and how much this mortality risk affects the optimal asset allocation./ Dans ce travail nous donnons une contribution à la litérature de l'allocation optimale du portefeuille en temps continu. En particulier, nous analysons le problème d'un investisseur qui veut maximiser la valeur espérée de l'utilité de sa richesse, avec un horizon temporel fini. En utilisant la théorie du contrôle optimal dynamique, on developpe un modèle dédié à l'analyse de l'allocation optimal de portefeuille pour un investisseur institutionnel tel qu'une banque, une compagnie d'assurance, un fond commun d'investissement ou un fond de pension. Un tel investisseur ne peut pas contrôler les contributions et les prelèvements du fond géré. En effet, même si l'approche classique optimise soit le portefeuille soit la consommation intertemporelle en considérant les prélèvements du fond dûs à la consommation comme une variable de contrôle, dans notre approche les flux de richesse qui diffèrent des coupons et dividends, sont tout simplement des variables d'état. On appellera ces variables "variables de background". De plus, notre analyse rend compte explicitement du risque d'inflation qui est généralement négligé par la literature sur l'allocation des actifs financiers. Dans ce contexte nous présentons une solution quasi-explicite pour l'investissement optimal sans spécifier acune forme fonctionnelle ni pour les dérives, ni pour les diffusions des équations stochastiques qui décrivent le marché financier, les variables de background et l'inflation. Nous supposons que l'attitude envers le risque de l'investisseur institutionnel est décrit par une fonction d'utilité croissante et concave, dont l'aversion au risque est absolument constante, relativement constante ou hyperbolique selons la structure du problème qui doit être resolu. Finalement nous analyson explicitement le cas d'un fond de pension qui veut maximiser la valeur espérée de sons surplus. Contrairement aux modèles qui étudient un investisseur qui est institutionnel mais pas actuarial, le cas d'un fond de pension requiert l'introduction de deux nouvelles characteristiques: (i) le comportement différent de la richesse du fond pendant les phases d'accumulation et de décumulation, et (ii) le risque de mortalité. Nous developpons un modèle afin de déterminer comment et combien le risque de mortalité affecte l'allocation optimale de portefeuille.

Do corporate bond spreads reflect fear of debt deflation? Most corporate bonds have fixed nominal face values, so unexpectedly low inflation raises firms' real debt burdens and increases default risk. The first chapter develops a real business cycle model with time-varying inflation risk and optimal, but infrequent, capital structure choice. In this model, more volatile or more procyclical inflation lead to quantitatively important credit spread increases. This is true even with inflation volatility as moderate as that in developed economies since 1970. Intuitively, this result obtains because inflation persistence generates large uncertainty about the price level at long maturities and because firms cannot adjust their capital structure immediately. We find strong empirical support for our model predictions in a panel of six developed economies. Both inflation volatility and the inflation-stock return correlation have varied substantially over time and across countries. They jointly explain as much variation in credit spreads as do equity volatility and the dividend-price ratio. Credit spreads rise by 15 basis points if either inflation volatility or the inflation-stock return correlation increases by one standard deviation. Firms counteract higher debt financing costs by adjusting their capital structure in times of higher inflation uncertainty. The second chapter empirically decomposes excess return predictability in inflation-indexed and nominal government bonds into liquidity, market segmentation, real interest rate risk and inflation risk. This chapter finds evidence for time-varying liquidity premia in Treasury Inflation Protected Securities (TIPS) and for time-varying liquidity premia in TIPS and for time-varying inflation risk premia in nominal bonds. The third chapter develops a pre-test for weak instruments in linear instrumental variable regression that is robust to heteroskedasticity and autocorrelation. Our test statistic is a scaled version of the regular first-stage F statistic. The critical values depend on the long-run variance-covariance matrix of the first stage. We apply our pre-test to the instrumental variable estimation of the Elasticity of Intertemporal Substitution and find that instruments previously considered not to be weak do not exceed our threshold.

This note examines the behavior of a competitive firm that faces joint price and inflation risk. Given that the price risk is negatively correlated with the inflation risk in the sense of expectation dependence, the firm optimally opts for an over-hedge if the firm's coefficient of relative risk aversion is everywhere no greater than unity. Furthermore, banning the firm from forward trading may induce the firm to produce more or less, depending on whether the price risk premium is positive or negative, respectively. While the price risk premium is unambiguously negative in the absence of the inflation risk, it is not the case when the inflation risk prevails. In contrast to the conventional wisdom, forward hedging needs not always promote production should firms take in inflation seriously.

This note examines the behavior of a competitive firm that faces joint price and inflation risk. Given that the price risk is negatively correlated with the inflation risk in the sense of expectation dependence, the firm optimally opts for an over-hedge if the firm's coefficient of relative risk aversion is everywhere no greater than unity. Furthermore, banning the firm from forward trading may induce the firm to produce more or less, depending on whether the price risk premium is positive or negative, respectively. While the price risk premium is unambiguously negative in the absence of the inflation risk, it is not the case when the inflation risk prevails. In contrast to the conventional wisdom, forward hedging needs not always promote production should firms take in inflation seriously.

The thesis focuses on the analysis of the impact of the inflation uncertainty on the reinsurance pricing, particularly on its measures of risk. Vector autoregression models are used to predict the medium-term inflation and simulate different inflation paths. The consideration of various scenarios of future inflation captured by the stochastic modelling increases the value at risk (VaR) and the tail value of risk (TVaR) of mean ceded loss to the reinsurer. The thesis founds that the inflation uncertainty measured by the stochastic inflation matters and it is important from risk management and hedging perspectives. As a result, additional loadings could be added to the price for the mitigation of the inflation risk. Although the effect of stochasticity of the future inflation is not significant on mean loss, it is the case for the risk of measures, especially for the contracts with high retention relatively to the underlying exposure. JEL Classification F12, F21, F23, H25, H71, H87 Keywords reinsurance pricing, inflation forecasting, inflation risk, long-tail line of business Title Macroeconomic Uncertainty: An Exogenous Risk in Reinsurance Pricing

This thesis aims at contributing to the study of the valuation of insurance liabilities and the management of the assets backing these liabilities. It consists of four parts, each devoted to a specific topic. In the first part, we study the pricing of a classical single premium life insurance contract with profit, in terms of a guaranteed rate on the premium and a participation rate on the (terminal) financial surplus. We argue that, given the asset allocation of the insurer, these technical parameters should be determined by taking explicitly into account the risk management policy of the insurance company, in terms of a risk measure such as the value-at-risk or the conditional value-at-risk. We then design a methodology that allows us to fix both parameters in such a way that the contract is fairly priced and simultaneously exhibits a risk consistent with the risk management policy. In the second part, we focus on the management of the surrender option embedded in most life insurance contracts. In Chapter 2, we argue that we should model the surrender time as a random time not adapted to the filtration generated by the financial assets prices, instead of assuming that the surrender time is an optimal stopping time as it is usual in the actuarial literature. We then study the valuation of insurance contracts with a surrender option in such a model. We here follow the financial literature on the default risk and in particular, the reduced-form models. In Chapter 3 and 4, we study the hedging strategies of such insurance contracts. In Chapter 3, we study their risk-minimizing strategies and in Chapter 4, we focus on their ``locally risk-minimizing' strategies. As a by-product, we study the impact of a progressive enlargement of filtration on the so-called ``minimal martingale measure'. The third part is devoted to the systematic mortality risk. Due to its systematic nature, this risk cannot be diversified through increasing the size of the portfolio. It is thus also important to study the hedging strategies an insurer should follow to mitigate its exposure to this risk. In Chapter 5, we study the risk-minimizing strategies for a life insurance contract when no mortality-linked financial assets are traded on the financial market. We here extend Dahl and Moller’s results and show that the risk-minimizing strategy of a life insurance contract is given by a weighted average of risk-minimizing strategies of purely financial claims, where the weights are given by the (stochastic) survival probabilities. In Chapter 6, we first study the application of the HJM methodology to the modelling of a longevity bonds market and describe a coherent theoretical setting in which we can properly define the longevity bond prices. Then, we study the risk-minimizing strategies for pure endowments and annuities portfolios when these longevity bonds are traded. Finally, the fourth part deals with the design of ALM strategies for a non-life insurance portfolio. In particular, this chapter aims at studying the risk-minimizing strategies for a non life insurance company when inflation risk and interest rate risk are taken into account. We derive the general form of these strategies when the cumulative payments of the insurer are described by an arbitrary increasing process adapted to the natural filtration of a general marked point process and when the inflation and the term structure of interest rates are simultaneously described by the HJM model of Jarrow and Yildirim. We then systematically apply this result to four specific models of insurance claims. We first study two ``collective' models. We then study two ``individual' models where the claims are notified at a random time and settled through time.

In the first essay, I decompose inflation risk into (i) a part that is correlated with real returns on the market portfolio and factors that determine investor’s preferences and investment opportunities and (ii) a residual part. I show that only the first part earns a risk premium. All nominal Treasury bonds, including the nominal money-market account, are equally exposed to the residual part except inflation-protected Treasury bonds, which provide a means to hedge it. Every investor should put 100% of his wealth in the market portfolio and inflation-protected Treasury bonds and hold a zero-investment portfolio of nominal Treasury bonds and the nominal money market account. In the second essay, I solve the dynamic asset allocation problem of finite lived, constant relative risk averse investors who face inflation risk and can invest in cash, nominal bonds, equity, and inflation-protected bonds when the investment opportunityset is determined by the expected inflation rate. I estimate the model with nominal bond, inflation, and stock market data and show that if expected inflation increases, then investors should substitute inflation-protected bonds for stocks and they should borrow cash to buy long-term nominal bonds. In the lastessay, I discuss how heterogeneity in preferences among investors withexternal non-addictive habit forming preferences affects the equilibrium nominal term structure of interest rates in a pure continuous time exchange economy and complete securities markets. Aggregate real consumption growth and inflation are exogenously specified and contain stochastic components thataffect their means andvolatilities. There are two classes of investors who have external habit forming preferences and different localcurvatures oftheir utility functions. The effects of time varying risk aversion and different inflation regimes on the nominal short rate and the nominal market price of risk are explored, and simple formulas for nominal bonds, real bonds, and inflation risk premia that can be numerically evaluated using Monte Carlo simulation techniques are provided.

Submitted by PEDRO ALVES (pguedesalves@gmail.com) on 2013-09-17T14:48:59Z No. of bitstreams: 1 Dissertacao pedro guedes alves final.pdf: 359622 bytes, checksum: 4ea301abbbeba3d60296bea87411ee79 (MD5) / Approved for entry into archive by Vitor Souza (vitor.souza@fgv.br) on 2013-10-09T15:39:12Z (GMT) No. of bitstreams: 1 Dissertacao pedro guedes alves final.pdf: 359622 bytes, checksum: 4ea301abbbeba3d60296bea87411ee79 (MD5) / Made available in DSpace on 2013-10-11T13:21:08Z (GMT). No. of bitstreams: 1 Dissertacao pedro guedes alves final.pdf: 359622 bytes, checksum: 4ea301abbbeba3d60296bea87411ee79 (MD5) Previous issue date: 2012-05-31 / Este trabalho busca medir a credibilidade do Banco Central Brasileiro. Utiliza-se como medida da credibilidade, a variação do prêmio de risco de inflação em função de surpresas inflacionárias de curto prazo no índice IPCA. Primeiro evidencia-se que as expectativas inflacionárias de médio prazo são afetadas pelas surpresas inflacionárias, este efeito é causado por dois motivos, a indexação da economia e/ou a falta de credibilidade da autoridade monetária. Em seguida verifica-se que as surpresas inflacionárias também tem efeito sobre o premio de risco de inflação o que indica falta de credibilidade do banco central. / This paper seeks to measure the credibility of the Brazilian Central Bank. It uses as a measure of credibility, the change in the inflation risk premium in terms of short-term inflationary surprises in the IPCA index. At first, it is shown that the medium-term inflation expectations are affected by inflation surprises, this effect is caused by two reasons, the indexation of the economy and/or lack of credibility of the monetary authority. Then it is observed that the inflation surprises also have an effect on the inflation risk premium, which indicates a lack of credibility of the central bank.

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2022 / Using the ARFIMA (autoregressive and fractionally integrated moving aver age) model extended with sGARCH (standard generalised autoregressive con ditional heteroscedasticity) and ’gjrGARCH (Glosten-Jagannathan-Runkle gen eralised autoregressive conditional heteroscedascity) innovations, fractional in tegration approach and state space model, this study has empirically examined persistency of inflation dynamics of Ghana and South Africa, the only two coun tries in Sub-Saharan Africa with Inflation Targeting (IT) monetary policy. The first part of the analysis employed monthly CPI (Consumer Price Index) in flation series for the period January 1971 to October 2014 obtained from the Bank of Ghana (BoG), and for the period January 1995 to December 2014 ob tained from Statistics South Africa. The second part involves the estimation of threshold effect of inflation on economic growth using annual data obtained from the IMF (International Monetary Fund) database for the period 1981 to 2014, for both countries. Results from the study showed that structural breaks, long memory and non linearities (or regime shifts) are largely responsible for inflation persistence, hence the ever-changing nature of inflation rates of Ghana and South Africa. ARFIMA(3,0.35,1)-‘gjrGARCH(1,1) under Generalised Error Distribution (GED) and ARFIMA(3,0.50,1)-‘gjrGARCH(1,1) under Student-t Distribution (STD) mod els provided the best fit for persistence in the conditional mean (or level) of CPI for Ghana and South Africa, respectively. The results from these models pro vided evidence of time-varying conditional mean and volatility in CPI inflation rates of both countries. The two models also revealed an asymmetric effect of inflationary shocks, where negative shocks appear to have greater impact than positive shocks, in terms of persistence on the conditional mean with time varying volatility. This thesis proposes a model that combines fractional integration with non linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa. We tested for non-linear deterministic terms in the context of fractional integration and esti mated the fractional differencing parameters, d to be 1.11 and 1.32 respectively, for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. New ev idence from this thesis depicts that inflation rate of Ghana is highly persistent and non-mean reverting, with an estimated fractional differencing parameter, d > 1.0, and will therefore require some policy action to steer inflation back to stability. However, the South African inflation series was found to be a cyclical process with an order of integration estimated to be d = 0.7, depicting mean reversion, with the length of the cycles approximated to last for 80 months. Finally, the thesis incorporated structural breaks, long memory, non-linearity, and some explanatory variables into a state space model and estimated the threshold effect of inflation on economic growth. The empirical results suggest that inflation below the estimated levels of 9% and 6% for Ghana and South Africa respectively, will be conducive for economic growth. The policy implications of these results for both countries are as follows. First, both series had similar properties responsible for inducing inflation persistence such as structural breaks, non-linearities, long memory and asymmetric re sponse to negatives shocks - but with varied degrees of magnitude. For both countries, the conditional mean and unobserved components such as volatility for both countries were found to be time-varying. This thesis, therefore, recom mends to the BoG and the South African Reserve Bank (SARB) - responsible for monetary policies, and the Finance Ministers of both governments - respon sible for fiscal policies, to take the above-mentioned properties into account in the formulation of their monetary policies. Second, the thesis recommends that the BoG and the SARB consolidate the IT policy, since keeping inflation below the targets set of 9% and 6%, respectively for Ghana and South Africa, will boost economic growth. Third, policymakers could also design measures (monetary and fiscal policies) such as increase in interest rates, credit control, and reduction of unnecessary expenditure, among others, to control inflation due to its adverse effects on market volatility. Even though an increase in interest rates could assist in curtailing the recent and anticipated increase in inflation rates in both countries, where targets have been missed by Ghana and South Africa, it will also be prudent to legislate monetary policies around demand-supply side since the problem of both coun tries appears to be more of a structuralist than a monetarist. It is, therefore, recommended that both countries tighten the IT monetary policy in order to re duce inflation persistence. This will eventually impact on poverty and income distribution with ramifications for economic growth and/or development. The fourth implication of these results is that governments and central banks should be mindful of the actions and decisions they take, in the sense that unguarded decisions and unnecessary alarms could raise uncertainties in the economy, which could, in turn, affect the future trajectory of inflation. Finally, the thesis recommends that governments of both countries strengthen the pri vate sector, which is the engine of growth. For small and open economies such as Ghana and South Africa, this will grow the economy through job creation and restore investor confidence. / National Research Foundation (NRF), Department of Science and Technology (DST), Telkom’s Tertiary Education Support Programme (TESP) and the NRF-DST Centre of Excellence for Mathematical and Statistical Sciences (CoE-MaSS)

Submitted by Maurício Tadeu Reis (mauricio_41@live.com) on 2018-09-04T14:10:20Z No. of bitstreams: 1 Dissertacao-04-09-2018.pdf: 942449 bytes, checksum: 506f00632a87d40c0d92c1996f1cf67f (MD5) / Rejected by Joana Martorini (joana.martorini@fgv.br), reason: ,, on 2018-09-04T15:07:20Z (GMT) / Submitted by Maurício Tadeu Reis (mauricio_41@live.com) on 2018-09-04T15:16:08Z No. of bitstreams: 1 Dissertacao-04-09-2018.pdf: 942449 bytes, checksum: 506f00632a87d40c0d92c1996f1cf67f (MD5) / Approved for entry into archive by Josineide da Silva Santos Locatelli (josineide.locatelli@fgv.br) on 2018-09-04T15:16:43Z (GMT) No. of bitstreams: 1 Dissertacao-04-09-2018.pdf: 942449 bytes, checksum: 506f00632a87d40c0d92c1996f1cf67f (MD5) / Approved for entry into archive by Isabele Garcia (isabele.garcia@fgv.br) on 2018-09-04T15:22:27Z (GMT) No. of bitstreams: 1 Dissertacao-04-09-2018.pdf: 942449 bytes, checksum: 506f00632a87d40c0d92c1996f1cf67f (MD5) / Made available in DSpace on 2018-09-04T15:22:27Z (GMT). No. of bitstreams: 1 Dissertacao-04-09-2018.pdf: 942449 bytes, checksum: 506f00632a87d40c0d92c1996f1cf67f (MD5) Previous issue date: 2018-08-09 / Neste trabalho serão estimadas diversas regressões para o prêmio de risco de inflação encontrado na economia brasileira, com dados entre janeiro 2006 e dezembro 2017. Adicionalmente, a inflação implícita terá uma seção de resultados semelhante ao encontrado para o prêmio de risco de inflação. Foram encontradas na literatura, tanto local quanto na estrangeira, poucas referências que tinham como tema central o prêmio de risco de inflação, a literatura encontrada é mais vasta ao buscarmos por inflação implícita ou taxa natural de juros. Os modelos construídos para mercados estrangeiros visam eliminar o problema da defasagem nos indexados de inflação dos títulos reais, como tanto no trabalho de Evans quanto de Grishchenko e Huang onde, para os mercados britânico e americano, respectivamente, aplicam um modelo que visava reduzir o ruído gerado pela defasagem no indexador de inflação. Para o mercado local, temos uma literatura mais focada em inflação implícita, no qual podemos notar em Vicente e Graminho que realizam a decomposição de todos os componentes da inflação implícita, inclusive o prêmio de risco de inflação. Foi possível tirar algumas conclusões sobre quais variáveis podem afetar o prêmio de risco de inflação e de qual forma, destas, destacou-se o CDS e as expectativas de inflação para períodos condizentes com os analisados para juros reais e nominais. / In this work many regressions towards the inflation risk premium for the Brazilian economy will be estimated, with data from January 2006 to December 2017. In addition to that, there will be a topic where we can find similar results for the implicit inflation as the ones obtained for the inflation risk premium. In the bibliography we found a few references for both local and foreign studies about the main topic, the inflation risk premium, the bibliography is more common to implicit inflation and natural interest rates. The models constructed for the foreign markets focused on minimizing the inflation lag problem on the indexed real bonds, both Evans's work and Grishchenko and Huang tried to minimize this problem with their models, for the British and American economies, respectively, their models tried to build an alternative real termstructure without this inflation lag. For the local market we found a bibliography more focused on implicit inflation, such as in Vicente and Graminho who studied the implicit inflation and all of its components, including the inflation risk premium. It was possible to take a few conclusions about some economic variables and its relation to inflation risk premium, if it exists. From these variables, we highlight the CDS and inflation expectations in consistent periods with those used for real and nominal interest rates.