Portfolio Optimization with Jumps and Unobservable Intensity Process
نویسندگان
چکیده
We consider a financial market with one bond and one stock. The dynamics of the stock price process allow jumps which occur according to a Markov-modulated Poisson process. We assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain. The investor’s aim is to maximize the expected utility of terminal wealth. Using a classical result from filter theory it is possible to reduce this problem with partial observation to one with complete observation. With the help of a generalized HamiltonJacobi-Bellman equation where we replace the derivative by Clarke’s generalized gradient, we identify an optimal portfolio strategy. Finally, we discuss some special cases of this model and prove several properties of the optimal portfolio strategy. In particular we derive bounds and discuss the influence of uncertainty on the optimal portfolio strategy.
منابع مشابه
Portfolio optimisation with jumps: Illustration with a pension accumulation scheme
In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lé...
متن کاملStock Portfolio Optimization Using Water Cycle Algorithm (Comparative Approach)
Portfolio selection process is a subject focused by many researchers. Various criteria involved in this process have undergone alterations over time, necessitating the use of appropriate investment decision support tools. An optimization approach used in different sciences is using meta-heuristic algorithms. In the present study, using Water Cycle Algorithm (WCA), a model was introduced for sel...
متن کاملExpected log-utility maximization under incomplete information and with Cox-process observations
We consider the portfolio optimization problem for the criterion of maximization of expected terminal log-utility. The underlying market model is a regime-switching diffusion model where the regime is determined by an unobservable factor process forming a finite state Markov process. The main novelty is due to the fact that prices are observed and the portfolio is rebalanced only at random time...
متن کاملPortfolio Optimization under Time-Varying Economic Regimes
Our paper aims to answer the question: Can the macroeconomic condition be used to better allocate investments among different sectors of a market? Motivated by classical Markowitz portfolio theory, and prior work in attempting to incorporate exogenous economic factors in portfolio optimization [1][2][3][4], we explore three approaches to dynamically rebalance a portfolio as market or economic r...
متن کاملThe Current Models of Credit Portfolio Management: A Comparative Theoretical Analysis
The present paper aimed at studying the current models of credit portfolio management. There are currently three types of models which consider the risk of credit portfolio: the structural models (Moody's KMV model, and Credit- Metrics model), the intensity models (the actuarial models) and the econometric models (the Macro-factors model). The development of these three types of models is based...
متن کامل