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7 papers · 1 filter
The probability of exceeding a piecewise deterministic barrier by the heavy-tailed renewal compound process
Zbigniew Palmowski, Martijn Pistorius
We analyze the asymptotics of crossing a high piecewise linear barriers by a renewal compound process with the subexponential jumps. The study is motivated by ruin probabilities of…
Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results
Florin Avram, Zbigniew Palmowski, Martijn R. Pistorius
Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of cla…
A two-dimensional ruin problem on the positive quadrant
Florin Avram, Zbigniew Palmowski, Martijn Pistorius
In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of th…
A Singular Control Model with Application to the Goodwill Problem
Andrew J. F. Jack, Timothy C. Johnson, Mihail Zervos
We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional Itô diffusion. The control effort that can be applied to this system tak…
Transformations of Markov Processes and Classification Scheme for Solvable Driftless Diffusions
Claudio Albanese, Alexey Kuznetsov
We propose a new classification scheme for diffusion processes for which the backward Kolmogorov equation is solvable in analytically closed form by reduction to hypergeometric equ…
An explicit Skorokhod embedding for spectrally negative Levy processes
Jan Obloj, Martijn Pistorius
We present an explicit solution to the Skorokhod embedding problem for spectrally negative Lévy processes. Given a process and a target measure satisfying an explicit admis…