In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian...

We show that the equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping known for convex performance criteria (see, for example, Karatzas and Shreve (1984)) continues to hold in a non convex problem provided a related discretionary...

We study the behavior of the critical price of an American put option near maturity in an exponential Lévy model. In particular, we prove that in situations where the limit of the critical price is equal to the strike price, the rate of convergence to the limit is linear if and only if the...

We give a complete and self-contained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American path dependent options. The framework is su±ciently general to include geometric Asian options with non-constant volatility and recent...

We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the...

The valuation theory for American Contingent Claims, due to Bensoussan (1984) and Karatzas (1988), is extended to deal with constraints on portfolio choice, including incomplete markets and borrowing/short-selling constraints, or with different interest rates for borrowing and lending. In the...

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions,...

In this work, we address an investment problem where the investment can either be made immediately or postponed to a later time, in the hope that market conditions become more favourable. In our case, uncertainty is introduced through market price. When the investment is undertaken, a fixed sunk...

Real options models characterized by the presence of ambiguity have been recently proposed. But based on recursive multiple-priors approaches to solve ambiguity, these seminal models reduce individual preferences to extreme pessimism by considering only the worst case scenario. In contrast, by...