The optimal control problem is considered for linear stochastic systems with a singular cost. A new uniformly convex structure is formulated, and its consequences on the existence and uniqueness of optimal controls and on the uniform convexity of the value function are proved. In particular, the...

The following backward stochastic Riccati differential equation (BSRDE in short) is motivated, and is then studied. Some properties are presented. The existence and uniqueness of a global adapted solution to a BSRDE has been open for the case D i 6= 0 for more than two decades. Our recent...

We consider the demand for state contingent claims in the presence of a zero-mean, nonhedgeable background risk. An agent is defined to be generalized risk averse if he/she reacts to an increase in background risk by choosing a demand function for contingent claims with a smaller slope. We show...

The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the filtration of the underlying Brownian motion is proved. This result is applied to the pricing of contingent claims. It allows to compare the prices of agents who have different...

We obtain the global existence and uniqueness result for a one-dimensional back- ward stochastic Riccati equation, whose generator contains a quadratic term of L (the second unknown component). This solves the one-dimensional case of Bismut- Peng's problem which was initially proposed by Bismut...

We consider two sequences of Markov chains induc- ing equivalent measures on the discrete path space. We estab- lish conditions under which these two measures converge weakly to measures induced on the Wiener space by weak solutions of two SDEs, which are unique in the sense of probability law....

We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.

While the stochastic volatility (SV) generalization has been shown to improvethe explanatory power compared to the Black-Scholes model, the empiricalimplications of the SV models on option pricing have not been adequately tested.The purpose of this paper is to first estimate a multivariate SV...

In this paper we introduce a new methodology to price American put options under stochastic interestrates. The method is a combination of an analytic approach and a binomial tree approach. We constructa binomial tree for the forward risk adjusted tree and calculate analytically the expected...

Taking a portfolio perspective on option pricing and hedging, we show that within the standard Black-Scholes-Merton framework large portfolios of options can be hedged without risk in discrete time. The nature of the hedge portfolio in the limit of large portfolio size is substantially different...