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On some stochastic control problems arising in models of optimal portfolio liquidation: I

Wednesday 1st October 2014 - 10:30 to 12:00
INI Seminar Room 2
Traditional financial market models assume that asset prices follow an exogenous stochastic process and that all transactions can be settled without any impact on market prices. The assumption that all trades can be carried out at exogenous prices is appropriate for small investors who trade only a negligible proportion of the average daily trading volume. Due to lack of liquidity, it is not always appropriate, though, for institutional investors trading large blocks of shares over a short time span. p> The analysis of optimal liquidation problems has received considerable attention in the mathematical finance and stochastic control literature in recent years. From a control theoretic perspective the main characteristic of optimization problems arising within the framework of portfolio liquidation is a strong terminal state constraint, the liquidation constraint, which induces a singular terminal value of the value function. Optimal liquidation problems therefore naturally lead to PDEs, respectively, BSPDEs in the non-Markovian framework, with singular terminal conditions.

We review recent existence and uniqueness of solutions results for PDEs and BSPDEs with singular terminal value arising in models of optimal portfolio liquidation under price sensitive market impact. Our models are flexible enough to allow for simultaneous trading in regular exchanges and dark pools.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons