We apply perturbation theory to solve the optimal control problem of an investor with time-additive power utility over intermediate consumption and final wealth. Under general conditions we show existence of a power series representation for the prevailing optimal consumption and investment...

We solve analytically the Merton's problem of an investor with time-additive power utility. For general state dynamics, we prove existence of two power series representations of the relevant optimal policies and value functions, which hold for all admissible risk aversion parameters. We...

We study in a general perspective the partial equilibrium incentives and the general equilibrium asset pricing implications of Value-at-Risk (VaR) regulation in continuous time economies with intermediate consumption, stochastic opportunity set, and heterogenous attitudes to risk. Our findings...

We apply perturbation methods to solve in closed form a class of robust control problems, implied by Anderson, Hansen and Sargent setting of a preference for robustness. In the constant investment opportunity set case, we obtain closed form power series solutions for the arising robust Bellman...

A generalized correlated random walk is a process X_k of partial sums of random variables Y_j such that (X,Y) forms a Markov chain. For a sequence X^n of such processes where each Y^n_j takes only two values, we prove weak convergence to a diffusion process whose generator is explicitly...

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and...

This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

This paper studies modelling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in...

We study the dynamic utility indifference value process p(X) when the usefulness of X is evaluated via a dynamic monetary concave utility functional (DMCUF) instead of von Neumann/Morgenstern expected utility. A DMCUF is minus a dynamic convex risk measure. The key tools for our investigations...