6 papers · 1 filter
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…
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…
Distributional equations and the ruin problem for the Sparre Andersen model with investments
Yuri Kabanov, Danil Legenkiy, Platon Promyslov
This note is an addendum to the work initiated by Eberlein, Kabanov, and Schmidt and developed further by Kabanov and Promyslov on the asymptotics of the ruin probabilities in the…