2015/04/10 by Olfa Draouil, Draouil, Olfa, Bernt Øksendal +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #math.OC #msc:60Gxx #msc:60H05 #msc:60H07 #msc:60H40 #msc:60J75 #msc:91G80 #msc:93E10 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1504.02581
arxiv created 2015/10/13 · arxiv updated 2015/10/14
We study optimal insider control problems, i.e. optimal control problems of stochastic systems where the controller at any time t in addition to knowledge about the history of the system up to this time, also has additional information related to a future value of the system. Since this puts the associated controlled systems outside the context of semimartingales, we apply anticipative white noise analysis, including forward integration and Hida-Malliavin calculus to study the problem. Combining this with Donsker delta functionals we transform the insider control problem into a classical (but parametrised) adapted control system, albeit with a non-classical performance functional. We establish a sufficient and a necessary maximum principle for such systems. Then we apply the results to obtain explicit solutions for some optimal insider portfolio problems in financial markets described by It\^ o-L' evy processes. Finally, in the Appendix we give a brief survey of the concepts and results we need from the theory of white noise, forward integrals and Hida-Malliavin calculus.