2018/11/27 by Marco Fuhrman, Fuhrman, Marco, Marie-Amélie Morlais +1 · 2 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Stochastic processes and financial applications #Climate Change Policy and Economics #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.1811.10886
We address a general optimal switching problem over finite horizon for a\nstochastic system described by a differential equation driven by Brownian\nmotion. The main novelty is the fact that we allow for infinitely many modes\n(or regimes, i.e. the possible values of the piecewise-constant control\nprocess). We allow all the given coefficients in the model to be\npath-dependent, that is, their value at any time depends on the past trajectory\nof the controlled system. The main aim is to introduce a suitable (scalar)\nbackward stochastic differential equation (BSDE), with a constraint on the\nmartingale part, that allows to give a probabilistic representation of the\nvalue function of the given problem. This is achieved by randomization of\ncontrol, i.e. by introducing an auxiliary optimization problem which has the\nsame value as the starting optimal switching problem and for which the desired\nBSDE representation is obtained. In comparison with the existing literature we\ndo not rely on a system of reflected BSDE nor can we use the associated\nHamilton-Jacobi-Bellman equation in our non-Markovian framework.\n