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We show that the problem of existence of equilibrium in Kyles continuous time insider trading model ([31]) can be tackled by considering a system of quasilinear parabolic equation and a Fokker-Planck equation coupled via a transport type constraint. By obtaining a stochastic representation for the solution of such a system, we show the well-posedness of solutions and study the properties of the equilibrium obtained for small enough risk aversion parameter. In our model, the insider has exponential type utility and the belief of the market on the distribution of the price at final time can be non-Gaussian.
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other b
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the returns dis
We consider the problem of finding Pareto-optimal allocations of risk among finitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measu
In this paper we consider the classical and Erlang(2) risk processes when the inter-claim times and claim amounts are dependent. We assume that the dependence structure is defined through a Farlie-Gumbel-Morgenstern (FGM) copula and show that the met
We study two-dimensional stochastic differential equations (SDEs) of McKean--Vlasov type in which the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. Such S