7 papers
Smoothness of the survival probability in models with a random environment: the annuity and mixed cases
Platon Promyslov
We consider the ruin problem for an insurance company investing its whole reserve in a risky asset whose parameters depend on a Markov random environment. Using the Green's functio…
Exact asymptotics of the ruin probability in the Sparre Andersen model
Platon Promyslov
For the Sparre Andersen non-life insurance model with investments in an arbitrary Lévy process, we establish the exact power-law asymptotics of the ruin probability $Ψ(u)\sim C^*…
Exact solution of the ruin problem in the Cramér--Lundberg model with proportional investment
Platon Promyslov, Maxim Romanov, Goluba Yurieva
The Cramér-Lundberg model with exponential claims and proportional investment is solved exactly: the integro-differential equation for the survival probability reduces to a doubly…
Existence of a classical solution to the integro-differential equation arising in the Cramér--Lundberg non-life insurance model with proportional investment
Platon Promyslov
This paper establishes that the survival probability in the non-life Cramér--Lundberg insurance model with proportional investment is a classical -solution of the associated…
Viscosity solutions of the integro-differential equation for the Cramér--Lundberg model with annuity payments and investments
Platon Promyslov
This note is an addendum to the work initiated by Promyslov on the integro-differential equation arising in the ruin problem for annuity payment models. First, the existence of vis…
On the integro-differential equation arising in the ruin problem for annuity payment models
Platon Promyslov
We study a ruin problem for an annuity model where a fixed fraction of capital is invested in a risky asset. Under weak assumptions on jumps, the ruin probability solves a second-o…