A topical problem is how to price and hedge claims on nontraded assets. A natural approach is to use for hedging purposes another similar asset or index which is traded. To model this situation, we introduce a second nontraded log Brownian asset into the well-known Merton investment model with...

This paper orders option prices under various well known martingale measures in an incomplete stochastic volatility model. The central result is a comparison theorem which proves convex option prices are decreasing in the market price of volatility risk, the parameter governing the choice of...

This paper presents a model of investment timing by risk averse managers facing incomplete markets and corporate control. Managers are exposed to idiosyncratic risks due to the dependence of their compensation on investment payoffs which are not spanned by other assets. We show that risk averse...

The aim of this paper is to investigate the properties of stochastic volatility models, and to discuss to what extent, and with regard to which models, properties of the classical exponential Brownian motion model carry over to a stochastic volatility setting. The properties of the classical...

This paper studies a variant of the contest model introduced by Seel and Strack. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and chooses when to stop it. The winner of the contest is the contestant who stops at the highest value....

In this article, we consider the optimal investment-consumption problem for an agent with preferences governed by Epstein-Zin stochastic differential utility who invests in a constant-parameter Black-Scholes-Merton market.The paper has three main goals: first, to provide a detailed introduction...

In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black-Scholes-Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write down a candidate value function and to use a verification...