Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting

2015/04/05 by Thomas Kruse, Kruse, T, Alexandre Popier +1 · 4 citations
Economics, Econometrics and Finance · Decision Sciences · Social Sciences · #Stochastic processes and financial applications #Risk and Portfolio Optimization #Insurance, Mortality, Demography, Risk Management

paper · pdf · doi:10.48550/arxiv.1504.01150

Abstract

We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +∞ with positive probability. We deal with equations on a general filtered probability space and with generators satisfying a general monotonicity assumption. With this minimal supersolution we then solve an optimal stochastic control problem related to portfolio liquidation problems. We generalize the existing results in three directions: firstly there is no assumption on the underlying filtration (except completeness and quasi-left continuity), secondly we relax the terminal liquidation constraint and finally the time horizon can be random.

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