319 citations · 464 across the 28 of their papers we have counts for
21 papers · 1 filter
On Dynamic Deviation Measures and Continuous-Time Portfolio Optimisation
Martijn Pistorius, Mitja Stadje
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we…
Randomisation and recursion methods for mixed-exponential Levy models, with financial applications
Aleksandar Mijatovic, Martijn Pistorius, Johannes Stolte
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times…
The distribution of the supremum for spectrally asymmetric Lévy processes
Zbigniew Michna, Zbigniew Palmowski, Martijn Pistorius
In this article we derive formulas for the probability and where is a spectrally positive Lévy process with infinit…
On Future Drawdowns of Lévy processes
E. J. Baurdoux, Z. Palmowski, M. R. Pistorius
For a given Lévy process and for fixed and we analyse the {\it future drawdown extremes} that ar…
Convergence of BSΔEs driven by random walks to BSDEs: the case of (in)finite activity jumps with general driver
Dilip Madan, Martijn Pistorius, Mitja Stadje
In this paper we present a weak approximation scheme for BSDEs driven by a Wiener process and an (in)finite activity Poisson random measure with drivers that are general Lipschitz…
Asymptotic independence of three statistics of maximal segmental scores
Aleksandar Mijatović, Martijn Pistorius
Let be an iid sequence with negative mean. The -segment is the subsequence and its \textit{score} is given by $\max\{\sum_{m+1}^nξ_i,0\…
Buffer-overflows: joint limit laws of undershoots and overshoots of reflected processes
Aleksandar Mijatović, Martijn Pistorius
Let be the epoch of first entry into the interval , , of the reflected process of a Lévy process , and define the overshoot and un…
Joint asymptotic distribution of certain path functionals of the reflected process
Aleksandar Mijatovic, Martijn Pistorius
Let be the first time the reflected process of a Levy processes crosses x>0. The main aim of the paper is to investigate the asymptotic dependence of the path functi…
Explicit solution of an inverse first-passage time problem for Lévy processes and counterparty credit risk
M. H. A. Davis, M. R. Pistorius
For a given Markov process and survival function on , the inverse first-passage time problem (IFPT) is to find a barrier function $b:\mathbb{R}^+\t…
On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation
Dilip Madan, Martijn Pistorius, Mitja Stadje
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk…
On matrix exponential approximations of the infimum of a spectrally negative Levy process
Florin Avram, Andras Horvath, M. R. Pistorius
We recall four open problems concerning constructing high-order matrix-exponential approximations for the infimum of a spectrally negative Levy process (with applications to first-…
On Gerber-Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function
F. Avram, Z. Palmowski, M. R. Pistorius
This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative Lévy process (in the absence of dividend p…
On the drawdown of completely asymmetric Levy processes
Aleksandar Mijatovic, Martijn R. Pistorius
The {\em drawdown} process of a completely asymmetric Lévy process is equal to reflected at its running supremum : . In this paper we explicit…
On additive time-changes of Feller processes
Aleksandar Mijatović, Martijn Pistorius
In this note we generalise the Phillips theorem on the subordination of Feller processes by Levy subordinators to the class of additive subordinators (i.e. subordinators with indep…
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…
Cramér asymptotics for finite time first passage probabilities of general Lévy processes
Zbigniew Palmowski, Martijn Pistorius
We derive the exact asymptotics of if and tend to infinity with constant, for a Lévy process that admits exponential moments. The proo…
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…
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…
On the optimal dividend problem for a spectrally negative Lévy process
Florin Avram, Zbigniew Palmowski, Martijn R. Pistorius
In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative Lévy process in the absence of dividend payments…
On maxima and ladder processes for a dense class of Levy processes
M. R. Pistorius
Consider the problem to explicitly calculate the law of the first passage time T(a) of a general Levy process Z above a positive level a. In this paper it is shown that the law of…