We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including value-at-risk (VaR), tail-value-at-risk (TVaR), and limited expected loss (LEL), these constraints can be both wealth-dependent (relative) and wealth-independent (absolute). The optimal ...

In this chapter we survey asset pricing in dynamic economies with heterogeneous, rational traders. By ‘rational’ we mean traders whose decisions can be described by preference maximization, where preferences are restricted to those which have an subjective expected utility (SEU) representation. By ’heterogeneous” we mean SEU traders with different and distinct payoff functions, discount factors...

We consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Lévy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strategies to the continuous-time counterpart. In addition, we provide and compa...

Using the savers-spenders theory developed by Mankiw (2000, AER), we propose microfoundations to the existence of rentiers in macroeconomic growth models. From an OLG model which acknowledges the great heterogeneity of consumer behavior apparent in the data, we capture the dynamic considerations of potential rentiers as a natural consequence of intertemporal utility maximization and we analyze ...

We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider’s information flow by using the theory of enlargement of filtrations and then obtain explicit logarit...

In this paper we study a class of robust utility maximization problem over a terminal wealth and consumption in a complete market. Using the backward stochastic differential equation theory (BSDE in short), we derive a comparison theorem to give a dynamic maximum principle for the optimal control of our problem. We prove the existence and uniqueness of an optimal strategy and we characterize it...

We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid technical conditions. The consequences...

We consider a financial market with a stock exposed to a counterparty risk inducing a drop in the price, and which can still be traded after this default time. We use a default-density modeling approach, and address in this incomplete market context the expected utility maximization from terminal wealth. We show how this problem can be suitably decomposed in two optimization problems in complet...