Utility maximization in a jump market model
نویسنده
چکیده
Abstract In this paper, we consider the classical problem of utility maximization in a financial market allowing jumps. Assuming that the constraint set is a compact set, rather than a convex one, we use a dynamic method from which we derive a specific BSDE. This being done, we aim at showing existence and uniqueness results for the introduced BSDE. This allows us finally to give an “explicit” expression of the value function and characterize optimal strategies for our problem.
منابع مشابه
Wealth Optimization and Dual Problems for Jump Stock Dynamics with Stochastic Factor
An incomplete financial market is considered with a risky asset and a bond. The risky asset price is a pure jump process whose dynamics depend on a jump-diffusion stochastic factor describing the activity of other markets, macroeconomics factors or microstructure rules that drive the market. With a stochastic control approach, maximization of the expected utility of terminal wealth is discussed...
متن کاملUtility Maximization in a Jump Market Model 1
In this paper, we consider the classical problem of utility maxi-mization in a financial market allowing jumps. Assuming that the constraint set of all trading strategies is a compact set, rather than a convex one, we use a dynamic method from which we derive a specific BSDE. To solve the financial problem, we first prove existence and uniqueness results for the introduced BSDE. This allows to ...
متن کاملEnergy Scheduling in Power Market under Stochastic Dependence Structure
Since the emergence of power market, the target of power generating utilities has mainly switched from cost minimization to revenue maximization. They dispatch their power energy generation units in the uncertain environment of power market. As a result, multi-stage stochastic programming has been applied widely by many power generating agents as a suitable tool for dealing with self-scheduling...
متن کاملAn extended existence result for quadratic BSDEs with jumps with application to the utility maximization problem
In this study, we consider the exponential utility maximization problem in the context of a jump-diffusion model. To solve this problem, we rely on the dynamic programming principle and we derive from it a quadratic BSDE with jumps. Since this quadratic BSDE2 is driven both by a Wiener process and a Poisson random measure having a Levy measure with infinite mass, our main work consists in estab...
متن کاملProgressive enlargement of filtrations and Backward SDEs with jumps
This work deals with backward stochastic differential equation (BSDE) with random marked jumps, and their applications to default risk. We show that these BSDEs are linked with Brownian BSDEs through the decomposition of processes with respect to the progressive enlargement of filtrations. We prove that the equations have solutions if the associated Brownian BSDEs have solutions. We also provid...
متن کامل