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<p>Aggressive fiscal and monetary policies by governments of countries and central banks in developed markets could somehow push inflation to some very high level in the long run. Due to the decreasing of pension fund benefits and increasing inflation rate, pension companies are selling inflation-linked products to hedge against inflation risk. Such companies are seriously considering the possible effects of inflation volatility on their investment, and some of them tend to include inflationary allowances in the pension payment plan. In this dissertation we study the management of pension funds of the defined contribution type in the presence of inflation-recession. We study how the fund manager maximizes his fund&rsquo / s wealth when the salaries and stocks are affected by inflation. In this regard, we consider the case of a pension company which invests in a stock, inflation-linked bonds and a money market account, while basing its investment on the contribution of the plan member. We use a benchmarking approach and martingale methods to compute an optimal strategy which maximizes the fund wealth.</p>

U.S. Treasury Securities are crucially important in many areas of finance. However, zero-coupon yields are not observable in the market. Even though published zero- coupon yields exist, they are sometimes not available for certain research topics or for high frequency. Recently, high frequency data analysis has become popular, and the GovPX database is a good source of tick data for U.S. Treasury securities from which we can construct zero-coupon yield curves. Therefore, we try to t zero- coupon yield curves from low frequency and high frequency data from GovPX by three different methods: the Nelson-Siegel method, the Svensson method, and the cubic spline method. Then, we try to retest the expectations hypothesis (EH) with new zero-coupon yields that are made from GovPX data by three methods using the Campbell and Shiller regression, the Fama and Bliss regression, and the Cochrane and Piazzesi regression. Regardless of the method used (the Nelson-Siegel method, the Svensson method, or the cubic spline method), the expectations hypothesis cannot be rejected in the period from June 1991 to December 2006 for most maturities in many cases. We suggest the possible explanation for the test result of the EH. Based on the overreaction hypothesis, the degree of the overreaction of spread falls over time. Thus, our result supports that the evidence of rejection of the EH has weaken over time. Also, we introduce a new estimation method for the stochastic volatility model of the short-term interest rates. Then, we compare our method with the existing method. The results suggest that our new method works well for the stochastic volatility model of short-term interest rates.

This paper considers dynamic optimal portfolio strategies of utility maximizing investors in the presence of risk constraints. In particular, we investigate the optimization problem with an additional constraint modeling bounded shortfall risk measured by Value at Risk or Expected Loss. Using the Black-Scholes model of a complete financial market and applying martingale methods we give analytic expressions for the optimal terminal wealth and the optimal portfolio strategies and present some numerical results.

The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the Expected Utility Loss. We generalize the findings our previous papers to this case. Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.

<p>Aggressive fiscal and monetary policies by governments of countries and central banks in developed markets could somehow push inflation to some very high level in the long run. Due to the decreasing of pension fund benefits and increasing inflation rate, pension companies are selling inflation-linked products to hedge against inflation risk. Such companies are seriously considering the possible effects of inflation volatility on their investment, and some of them tend to include inflationary allowances in the pension payment plan. In this dissertation we study the management of pension funds of the defined contribution type in the presence of inflation-recession. We study how the fund manager maximizes his fund&rsquo / s wealth when the salaries and stocks are affected by inflation. In this regard, we consider the case of a pension company which invests in a stock, inflation-linked bonds and a money market account, while basing its investment on the contribution of the plan member. We use a benchmarking approach and martingale methods to compute an optimal strategy which maximizes the fund wealth.</p>

Magister Scientiae - MSc / Aggressive fiscal and monetary policies by governments of countries and central banks in developed markets could somehow push inflation to some very high level in the long run. Due to the decreasing of pension fund benefits and increasing inflation rate, pension companies are selling inflation-linked products to hedge against inflation risk. Such companies are seriously considering the possible effects of inflation volatility on their investment, and some of them tend to include inflationary allowances in the pension payment plan. In this dissertation we study the management of pension funds of the defined contribution type in the presence of inflation-recession. We study how the fund manager maximizes his fund's wealth when the salaries and stocks are affected by inflation. In this regard, we consider the case of a pension company which invests in a stock, inflation-linked bonds and a money market account, while basing its investment on the contribution of the plan member. We use a benchmarking approach and martingale methods to compute an optimal strategy which maximizes the fund wealth. / South Africa

近年來在金融市場上出現了新型的金融衍生性商品，這些衍生性商品相當於一般的共同基金，但是額外鑲嵌了喊價選擇權，可以使投資人在市場表現不理想的時候，還能拿回一部份的本金；而在市場表現良好時，可以重置保本的水準來鎖定既得的利潤。因此新型的這類商品更容易吸引投資人。 　　分離基金便是這樣的商品，它募集投資大眾的資金進行投資，它不但提供保本的承諾，同時給予隨時重置保本水準的權利。然而，對發行商而言，它的風險相當地高，因此本篇論文將利用Martingale（平賭過程）的方法，針對這類商品鑲嵌的喊價選擇權來進行理論模型的推導、經濟意涵的分析、數值方法的評價，並且提出重要的避險策略。 / In recent years, there have been a lot of derivatives similar with mutual funds which guarantee that not only should investors receive a minimum benefit after a certain period of time, but also be provided with the reset right . Whenever investors reset, they can change a minimum benefit at the higher guarantee level. 　　Those kinds of funds are known as segregated funds in Canada. This paper develops a pricing model of shout options which are embedded in segregated funds by means of martingale method and it offers a hedge strategy for writers.

In this study, general geometric Levy market models are considered. Since these models are, in general, incomplete, that is, all contingent claims cannot be replicated by a self-financing portfolio consisting of investments in a risk-free bond and in the stock, it is suggested that the market should be enlarged by artificial assets based on the power-jump processes of the underlying Levy process. Then it is shown that the enlarged market is complete and the explicit hedging portfolios for claims whose payoff function depends on the prices of the stock and the artificial assets at maturity are derived. Furthermore, the portfolio optimization problem is considered in the enlarged market. The problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. It is shown that for particular choices of the equivalent martingale measure in the market, the optimal portfolio only consists of bonds and stocks. This corresponds to completing the market with additional assets in such a way that they are superfluous in the sense that the terminal expected utility is not improved by including these assets in the portfolio.

This paper considers dynamic optimal portfolio strategies of utility maximizing investors in the presence of risk constraints. In particular, we investigate the optimization problem with an additional constraint modeling bounded shortfall risk measured by Value at Risk or Expected Loss. Using the Black-Scholes model of a complete financial market and applying martingale methods we give analytic expressions for the optimal terminal wealth and the optimal portfolio strategies and present some numerical results.