We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an R-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial differential equation (BSPDE) related directly to the primal problem and show th...

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e. a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredi...

Existing models of financial market prices typically assume that investors are informed with economic data and that wealth maximization motivates them. This paper considers the social dimensions of investing and the effect that this additional motivation has on the evolution of prices in a multi-agent model of an equity market. Agents in this model represent both economically informed investors...

We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (asmodeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. Simple sufficient conditions are given for...

In this work, we examine the combined problem of optimal portfolio selection rules for an insurer in a continuous time model where surplus insurance company is modelled as compound Poisson process. The can invest its risk free asset and risky asset, governed by Black-Scholes equation. According to utility theory, financial market investors are facing uncertainty, investor not concerned with wea...

Dybvig ? introduced the interesting problem of how to construct in the cheapest possible way a terminal wealth with desired distribution. This idea has induced a series of papers concerning generality, consequences and applications. As the optimized claims typically follow the trend in the market, they are not useful for investors who wish to use them to protect an existing portfolio. For this ...