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[01340] Mathematical finance without probability

  • Session Time & Room : 1C (Aug.21, 13:20-15:00) @D514
  • Type : Contributed Talk
  • Abstract : We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral and that generic domain of functional calculus is inherently arbitrage-free. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. We apply the transition principle of Isaacs in differential games and obtain a verification theorem for the optimal solution, which is characterised by a fully non-linear path-dependent equation. For the Asian option, we obtain explicit solution.
  • Classification : 91G99, 91-10, Mathematical finance in continuous-time, model uncertainty
  • Format : Talk at Waseda University
  • Author(s) :
    • Henry Chiu (Imperial College London)