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Full-Text Articles in Physical Sciences and Mathematics
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If uα(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that limα→0αuα(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.
Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi
Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi
Mathematics Faculty Research Publications
In this paper, we consider the problem of super-replication under portfolio constraints in a Markov framework. More specifically, we assume that the portfolio is restricted to lie in a convex subset, and we show that the super-replication value is the smallest function which lies above the Black-Scholes price function and which is stable for the so-called face lifting operator. A natural approach to this problem is the penalty approximation, which not only provides a constructive smooth approximation, but also a way to proceed analytically.