Browsing by Author "Pinheiro, D."
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- Contingent claim pricing through a continuous time variational bargaining schemePublication . Azevedo, N.; Pinheiro, D.; Xanthopoulos, S. Z.; Yannacopoulos, A. N.We consider a variational problem modelling the evolution with time of two probability measures representing the subjective beliefs of a couple of agents engaged in a continuous-time bargaining pricing scheme with the goal of finding a unique price for a contingent claim in a continuous-time financial market. This optimization problem is coupled with two finite dimensional portfolio optimization problems, one for each agent involved in the bargaining scheme. Under mild conditions, we prove that the optimization problem under consideration here admits a unique solution, yielding a unique price for the contingent claim.
- Contingent claim pricing through a continuous time variational bargaining schemePublication . Azevedo, N.; Pinheiro, D.; Xanthopoulos, S. Z.; Yannacopoulos, A. N.We consider a variational problem modelling the evolution with time of two probability measures representing the subjective beliefs of a couple of agents engaged in a continuous-time bargaining pricing scheme with the goal of finding a unique price for a contingent claim in a continuous-time financialmarket. This optimization problem is coupled with two finite dimensional portfolio optimization problems, one for each agent involved in the bargaining scheme. Undermild conditions, we prove that the optimization problem under consideration here admits a unique solution, yielding a unique price for the contingent claim.
- Dynamic programming for a Markov-switching jump–diffusionPublication . Azevedo, N.; Pinheiro, D.; Weber, G.-W.We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.