Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging

We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the underlying filtration is noncontinuous. This includes results on portfolio optimization under an additional liability and on dynamic utility indifference valuation and partial hedging in incomplete financial markets which are exposed to risk from unpredictable events. In particular, we characterize the limiting behavior of the utility indifference hedging strategy and of the indifference value process for vanishing risk aversion.Comment: Published at http://dx.doi.org/10.1214/105051606000000475 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic Optimization for Financial Decision Making: Portfolio Selection Problem [QA402.5. K45 2008 f rb].

Tesis ini mengaplikasikan pengoptimuman berstokastik sebagai penyelesaian kepada masaalah pemilihan portfolio. Pemilihan portfolio merupakan satu bidang penting dalam pembuatan keputusan kewangan. Ciri penting bagi masaalah dalam pasaran kewangan umumnya terpisah dan tertakrif dengan jelas. In this thesis stochastic optimization was applied to solve portfolio selection problem. Portfolio selection problem is one of the important areas in financial decision making. An important distinguishing feature of problems in financial markets is that they are generally separable and well defined

The possibilities and consequences of investment decisions by stepwise optimization

The paper deals with the application of stochastic optimization principles for investment decision making. The authors present the investment management system based on an adequate portfolio model. For optimal portfolio construction and stock selection, the method of stochastically informative expertise and ranging is used. Investment portfolios in equity and currency markets are formed considering investor risk tolerance and risk preference level, as well as an individual utility function. Investment portfolios are constructed according to three criteria: return, risk, and reliability. The markets of Germany, the USA, and China, as well as foreign exchange markets, are analysed. The results reveal the efficient investment possibilities in the mentioned markets, allowing to reach investment return substantially exceeding market index return. Along with that, an innovative stochastic clustering methodology for investment assets is proposed. The obtained results are of great value for individual as well as institutional investors and are a suitable means to form efficient investment strategies in financial markets

Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization.

In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incomplete financial markets whose dynamics are governed by continuous semimartingales. Adapting standard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability at maturity. We illustrate our study by numerical simulations for selected examples. As a byproduct we prove existence of a solution to a very particular quadratic growth BSDE with unbounded terminal condition. This complements results on this topic obtained in [6, 7, 8].numerical scheme; stochastic optimal control; utility optimization; quadratic growth; distortion transformation; logarithmic transformation; BSPDE; BSDE;

Portfolio optimization of stochastic volatility models through the dynamic programming equations

In this work we study the problem of portfolio optimization in markets with stochastic volatility.The optimization criteria considered consists in the maximization of the utility of terminal wealth.The most usual method to solve this type of problem passes by the solution of an equation with partial derivatives,deterministic and nonlinear, named the Hamilton-Jacobi-Bellman equation (HJB) or the dynamic programming equation. One of the biggest challenges consists in verifying that the solution to the HJB equation coincides with the payoof the optimal portfolio.These results are known as verication theorems.In this sense,we follow the approach by Kraft[13],generalizing the verication theorems for more general utility functions. The most significant contribution of this work consists in the resolution of the optimal portfolio problem for the 2-hypergeometric stochastic volatility model considering power utilities. Specifically we obtain a Feynman-Kac formula for the solution of the HJ Bequation.Based on this stochastic representation weapply the Monte Carlo method to approximate the solution to the HJB equation,which if it sufifciently regular it coincides with the payoff function of the optimal portfolio

On the Measurement of financial market integration.

The paper presents sorne vector optimization problems to measure arbitrage and integration of financial markets. This new approach may be applied under static or dynamic asset pricing assumptions and leads to both, numerical and stochastic integration measures. Thus, the paper provides a new methodology in a very general setting, allowing many instruments in each market to test optimal arbitrage portfolios depending on the state of nature and the date. Markets with frictions are also analyzed, and sorne empirical results are presented.El artículo aplica la optimización vectorial para introducir nuevos procedimientos que miden el nivel de arbitraje e integración de mercados financieros. Las técnicas son aplicables tanto bajo supuestos estáticos, como bajo supuestos dinámicos de valoración de activos. Por consiguiente el nivel de generalidad es alto, y se proporcionan instrumentos que permiten determinar estrategias de arbitraje óptimas de carácter dinámico y estocástico. Finalmente, también se analizan los mercados con fricciones y se presentan los resultados de algunas contrastaciones empíricas.Vector optimization; Arbitrage portfolio; Dual problem; Pricing rule;

Portfolio Selection in Incomplete Markets with Utility Maximisation

The problem of maximizing the expected utility is well understood in the context of a complete financial market. This dissertation studies the same problem in an arbitrage-free yet incomplete market. Jin and Zhou have characterized the set of the terminal wealths that can be replicated by admissible portfolios. The problem is then transformed into a static optimization problem. It is proved that the terminal wealth is attainable for all utility functions when the market parameters are deterministic. The optimal portfolio is obtained explicitly when the utility function is logarithmic even if the market parameters follow stochastic processes. However we do not succeed in extending this result to the power utility function