2010/01/19 by Boualem Djehiche, Djehiche, Boualem, Saïd Hamadène +4
Economics, Econometrics and Finance · Engineering · Mathematics · #60G40 #62P20 #91B99 #93E20 #Capital Investment and Risk Analysis #Electric Power System Optimization #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:60G40 #msc:62P20 #msc:91B99 #msc:93E20 #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1001.3289
arxiv created 2010/01/19 · openalex publication_date 2010/01/19 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We then construct both a minimal and a maximal solutions using an approximation scheme of the associated system of reflected backward SDEs. When the dependence of the cash-flows on the sources of uncertainty, such as fluctuation market prices, assumed to evolve according to a diffusion process, is made explicit, we also obtain a connection between these solutions and viscosity solutions of a system of variational inequalities (VI) with interconnected obstacles. We also provide two counter-examples showing that uniqueness of solutions of (VI) does not hold in general.