This dissertation consist of three contributions to financial and insurance mathematics. The first part considers numerical methods for dynamic portfolio optimisation in the expected utility model. The aim is to compare the risk-neutral computational approach (RNCA) also known as the martingale approach to stochastic dynamic programming (SDP) in a discrete-time setting. The main idea of the RNCA is to use the completeness and the arbitrage free properties of the market to compute the optimal consumption rules and then determine the trading strategy that finance this optimal consumption. In contrast, SDP solves for the optimal consumption and investment rules simultaneously using backward recursion and the principle of optimality. The setting that we consider is a discrete time and state space lattice. We provide some new theoretical results relating to the Hyperbolic Absolute Risk Aversion class of utility functions as well as propose a straightforward implementation of RNCA in binomial and trinomial lattices. Moreover, instead of discretizing the Hamilton-Jacobi-Bellman equation with possibly more than one state variable, we use symbolic algorithms to implement stochastic dynamic programming. This new approach provides a simpler numerical procedure for computing optimal consumption-investment policies. A comparison of the RNCA with SDP demonstrates the superiority of the RNCA in terms of computation. The second part considers the pricing of contingent claims using an approach developed and applied in applied in insurance. This approach utilize probability distortion functions as the dual of the utility functions used in financial theory. The main idea of the dual theory is to distort the subjective probabilities rather than outcomes to express the investor????????s risk aversion. In the first part, the RNCA for asset allocation uses the same principle as risk-neutral valuation for derivative pricing. The idea of the second part of this research is to show that the risk-neutral valuation can be recovered from the probability distortion function approach, thereby establishing consistency between the insurance and the financial approaches. We prove that pricing contingent claims under the real world probability measure using an appropriate distortion operator produces arbitrage-free prices when the underlying asset prices are log-normal. We investigate cases when the insurance-based approach fails to produce arbitrage-free prices and determine the appropriate distortion operator under more general assumptions than those used in Black-Scholes option pricing. In the third part we introduce dynamic portfolio optimisation with risk measures based on probability distortion function and provide a formal treatment of this class of risk measures. We employ the RNCA to study the consumption-investment problem in discrete time with preferences consistent with Yaari????????s dual (non-expected utility) theory of choice. As an application, we first consider risk measures based on the Proportional Hazard Transform that treats the upside and downside of the risk differently and secondly a risk measure based on the standard Normal cumulative distribution function. When the objective is to maximise a dual utility of wealth, and the underlying security returns are normal, the efficient frontier is found to be the same as in the mean-variance portfolio problem for an equivalent risk tolerance. When the objective is to maximise a dual utility of consumption, then ????????plunging???????????? behaviour occurs ( investing everything is the risky asset). Other properties of the optimal consumption-investment policies in the dual theory are also investigated and discussed.

Thesis (Ph. D.)--Ohio State University, 1984. / Includes vita. Includes bibliographical references (leaves 100-104). Available online via OhioLINK's ETD Center.

Thesis (Ph. D.)--University of Chicago Graduate School of Business, August 1999. / Includes bibliographical references. Also available on the Internet.

Project (M.A.) - Simon Fraser University, 2005. / Project (Dept. of Economics) / Simon Fraser University. Also issued in digital format and available on the World Wide Web.

Thesis (M.S.)--University of Nevada, Reno, 2008. / "December, 2008." Includes bibliographical references (leaves 23-24). Library also has microfilm. Ann Arbor, Mich. : ProQuest Information and Learning Company, [2009]. 1 microfilm reel ; 35 mm. Online version available on the World Wide Web.

Not available / text

This thesis examines risk factors in the UK Stock Market. This objective is achieved by testing the validity of the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). The models were tested using data for the period between 1972 to 1993. Test of the CAPM was conducted by examining the relationship between stocks returns and systematic risk as measured by beta. By regressing returns against estimates of beta, the results showed that for the overall period the relationship was negative and the estimated risk premium is smaller than the observed risk premium. The results in sub-periods also failed to validate the model. However, examining the results under up and down-market conditions, showed some support to the usefulness of beta. Beta is a good predictor of average returns under down-market conditions as well as under extreme up-market conditions. Test of the APT entails the detennination on the number of factors, estimating the sensitivities or risks of stocks to these factors and finally the pricing of these risks. This study used the Principal Components Analysis (PCA) for the first two procedures. A two stage PCA was performed specifically for short sub-periods of data. The stability of the factor structure across sub-periods was also examined. For the third procedure, a cross-sectional regression between returns and the sensitivities was performed and the risk premia was estimated. The results showed that the number of factors were consistent across sub-periods. A PCA on any sample of stocks cou1l produce a first factor that is common among stocks, while other factors are more sample specific. The study found at least one significant risk premium in all the sub-periods. The first factor was the most likely to produce a significant risk premium. The sensitivities of the stocks to the factors were found to differ across sub-periods, but the risk premia remain constant. This suggests the factor structure may be stable. This thesis then identifies the economic nature of the factors. The factors were regressed against a selection of macroeconomic variables. The result showed that the first factor is related to stock market return, money supply, US and European exchange rates and dividend yield. The first factor from small size firms and low beta stocks are strongly related than usual to money supply. The second factor is related to default risk, term structure and stock market returns.

The purpose of this thesis is to provide new evidence on the pricing of foreign exchange risk in the stock market by testing international asset pricing models (IAPMs) under varying market structures and different exchange rate measures. It is composed of three essays. In the first essay, I test unconditional asset pricing models with exchange risk using country, portfolio and firm level data from nine emerging markets (EMs). It is shown that unlike the case for developed markets where unconditional tests often fail to detect a significant exchange risk premium in stock returns, exchange risk is unconditionally priced in EMs. However, when local market risk is introduced in the model to take into account potential segmentation effects, exchange risk premia are totally subsumed by local risk premia for most countries especially at the firm level. The second essay examines the significance of exchange risk in conditional IAPMs using multivariate GARCH-in-Mean specification and time varying prices of risk. The model tested assumes partial integration and uses real exchange rates to account for both inflation risk and nominal exchange risk. The main empirical results support the hypothesis of significant exchange risk premia in EMs equity returns even after accounting for local market risk. The exchange risk premia are also economically significant as they represent on average 18 percent of total premium, and may reach up to 45 percent of total premium for some countries over sub-periods. In the third essay, I test for the pricing of exchange risk in stock returns using globally diversified sector portfolios. The purpose of this test is to examine the effect of cross-currency diversification on the global price of foreign exchange risk. Since there is no previous evidence on this issue, I use data on the G7 countries and EMs. The results suggest that the effects of exchange risk may be less significant in pricing global assets such as global s

This dissertation consist of three contributions to financial and insurance mathematics. The first part considers numerical methods for dynamic portfolio optimisation in the expected utility model. The aim is to compare the risk-neutral computational approach (RNCA) also known as the martingale approach to stochastic dynamic programming (SDP) in a discrete-time setting. The main idea of the RNCA is to use the completeness and the arbitrage free properties of the market to compute the optimal consumption rules and then determine the trading strategy that finance this optimal consumption. In contrast, SDP solves for the optimal consumption and investment rules simultaneously using backward recursion and the principle of optimality. The setting that we consider is a discrete time and state space lattice. We provide some new theoretical results relating to the Hyperbolic Absolute Risk Aversion class of utility functions as well as propose a straightforward implementation of RNCA in binomial and trinomial lattices. Moreover, instead of discretizing the Hamilton-Jacobi-Bellman equation with possibly more than one state variable, we use symbolic algorithms to implement stochastic dynamic programming. This new approach provides a simpler numerical procedure for computing optimal consumption-investment policies. A comparison of the RNCA with SDP demonstrates the superiority of the RNCA in terms of computation. The second part considers the pricing of contingent claims using an approach developed and applied in applied in insurance. This approach utilize probability distortion functions as the dual of the utility functions used in financial theory. The main idea of the dual theory is to distort the subjective probabilities rather than outcomes to express the investor????????s risk aversion. In the first part, the RNCA for asset allocation uses the same principle as risk-neutral valuation for derivative pricing. The idea of the second part of this research is to show that the risk-neutral valuation can be recovered from the probability distortion function approach, thereby establishing consistency between the insurance and the financial approaches. We prove that pricing contingent claims under the real world probability measure using an appropriate distortion operator produces arbitrage-free prices when the underlying asset prices are log-normal. We investigate cases when the insurance-based approach fails to produce arbitrage-free prices and determine the appropriate distortion operator under more general assumptions than those used in Black-Scholes option pricing. In the third part we introduce dynamic portfolio optimisation with risk measures based on probability distortion function and provide a formal treatment of this class of risk measures. We employ the RNCA to study the consumption-investment problem in discrete time with preferences consistent with Yaari????????s dual (non-expected utility) theory of choice. As an application, we first consider risk measures based on the Proportional Hazard Transform that treats the upside and downside of the risk differently and secondly a risk measure based on the standard Normal cumulative distribution function. When the objective is to maximise a dual utility of wealth, and the underlying security returns are normal, the efficient frontier is found to be the same as in the mean-variance portfolio problem for an equivalent risk tolerance. When the objective is to maximise a dual utility of consumption, then ????????plunging???????????? behaviour occurs ( investing everything is the risky asset). Other properties of the optimal consumption-investment policies in the dual theory are also investigated and discussed.

Thesis (M.A.)--Dalhousie University (Canada), 2007. / Includes bibliographical references.