Analysis of optimal portfolio on finite and small time horizons for a stochastic volatility market model
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change from its current value. We consider an incomplete stochastic volatility market model, that is driven by both a Brownian motion and a jump process. At first, we obtain a closed-form formula for an approximation to the optimal portfolio in a small-time horizon. This is obtained by finding the associated Hamilton-Jacobi-Bellman integro-differential equation and then approximating the value function by constructing appropriate super-solution and sub-solution. It is shown that the true value function can be obtained by sandwiching the constructed super-solution and sub-solution. We also prove the accuracy of the approximation formulas. Finally, we provide a procedure for generating a close-to-optimal portfolio for a finite time horizon.
Code (0)
등록된 구현이 없습니다.
Tasks
Portfolio OptimizationSimilar Papers 제목 키워드 기반
Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets
In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bell…
Portfolio OptimizationExponential utility maximization in small/large financial markets
Obtaining utility maximizing optimal portfolios in closed form is a challenging issue when the return vector follows a more general distribution than the normal one. In this note, we give closed form expressions, in mark…
Portfolio OptimizationLog-optimal portfolio after a random time: Existence, description and sensitivity analysis
In this paper, we consider an informational market model with two flows of informations. The smallest flow F, which is available to all agents, is the filtration of the initial market model(S,F,P), where S is the assets'…
SensitivityInfinite dimensional portfolio representation as applied to model points selection in life insurance
We consider the problem of seeking an optimal set of model points associated to a fixed portfolio of life insurance policies. Such an optimal set is characterized by minimizing a certain risk functional, which gauges the…
Log-optimal portfolio and numéraire portfolio for market models stopped at a random time
This paper focuses on num\'eraire portfolio and log-optimal portfolio (portfolio with finite expected utility that maximizes the expected logarithm utility from terminal wealth), when a market model $(S,\mathbb F)$ -spec…