From "simple" stochastic control problems to "more realistic" ones:
an example from portfolio theory
In this talk we take an example from life-cycle portfolio theory
(modelled as a stochastic optimal control problem)
where we see how different economic questions, possibly arising from experimental data,
bring to formulate and study more complex problems, in particular
models which display path dependency and/or Mc Kean - Vlasov type dynamics.
Ongoing results on such problems will be presented.
We will discuss, depending on the available time, the following modelling levels.
Level 1: Lifecycle portfolio with Labor Income
Level 2: Lifecycle portfolio with Path-Dependent Labor Income (History dependent wages)
Level 3/1: Lifecycle portfolio with Path-Dependent Labor Income with uncertainty on parameters
(Taking account of estimation errors)
Level 3/2: Lifecycle portfolio with Path-Dependent Labor Income with Mc Kean-Vlasov type dynamics
(Taking account of the effect of the environment: "Keeping up with the Joneses")
Based on joint papers/work in progress with various authors
( Biagini, Biffis, Cosso, Djeiche, Kharroubi, Pham, Prosdocimi, Rosestolato, Zanco, Zanella).
Dr. Yvain BRUNED (University of Edinburgh)
15th of October
BPHZ renormalisation and vanishing subcriticality limit of the fractional $\Phi^3_d$ model.
In this talk, we consider the fractional $\Phi^3_d$ model which is a stochastic PDEs on the d-dimensional torus
with fractional Laplacian and quadratic nonlinearity driven by space-time white noise.
We obtain precise asymptotics on the renormalisation counterterms as the mollification parameter becomes small and the parameter of the fractional Laplacian approaches its critical value.
Multilevel Picard approximations for high-dimensional semilinear parabolic partial differential equations
We present new approximation methods for high-dimensional semilinear parabolic PDEs. A key idea of our methods is to combine multilevel approximations with Picard fixed-point approximations. We prove in the case of semilinear heat equations with Lipschitz continuous nonlinearities that the computational effort of one of the proposed methods grows polynomially both in the dimension and in the reciprocal of the required accuracy. We illustrate the efficiency of the approximation methods by means of numerical simulations. The talk is based on joint works with Weinan E, Martin Hutzenthaler, Arnulf Jentzen, Tuan Nguyen and Philippe Von Wurstemberger.
Prof. Jacco THIJSSEN (University of York)
29th of October
Predatory Pricing and the Value of Corporate Cash Holdings
We analyze the interaction between firms' payout policies and their decisions in product markets in a continuous-time stochastic game between two firms. One of these is financially constrained, whereas the other is not. Contrary to the standard literature we allow firms to choose production and payout strategies, and focus on the effect of predation incentives on both. We find that predation induces fewer dividend payouts. Furthermore, the liquidity position of the constrained firm has an economically significant effect on the production choices of both firms and, thus, on the evolution of profits, cash holdings and stock returns.