2 citations · 2 across the 12 of their papers we have counts for
15 papers
Pathwise Convergence of a Modular Simulation Scheme for Hybrid SDEs with Memory
Oscar Peralta
This work introduces hybrid stochastic differential equations with memory (mH-SDEs), a new class of stochastic systems where transition rates depend on the joint history of both Eu…
Ruin-dependent bivariate stochastic fluid processes
Hamed Amini, Andreea Minca, Oscar Peralta
This paper presents a novel model for bivariate stochastic fluid processes that incorporate a ruin-dependent behavioral switch. Unlike typical models that assume a shared underlyin…
Wong--Zakai approximation of regime-switching SDEs via rough path theory
Jasper Barr, Giang T. Nguyen, Oscar Peralta
This paper investigates the convergence of Wong--Zakai approximations to regime-switching stochastic differential equations, generated by a collection of finite-variation approxima…
Duration-dependent stochastic fluid processes and solar energy revenue modeling
Hamed Amini, Andreea Minca, Oscar Peralta
We endow the classical stochastic fluid process with a duration-dependent Markovian arrival process (DMArP). We show that this provides a flexible model for the revenue of a solar…
Space-grid approximations of hybrid stochastic differential equations and first passage properties
Hansjoerg Albrecher, Oscar Peralta
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the syste…
Strongly convergent homogeneous approximations to inhomogeneous Markov jump processes and applications
Martin Bladt, Oscar Peralta
The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. Ho…
Multivariate matrix-exponential affine mixtures and their applications in risk theory
Eric C. K. Cheung, Oscar Peralta, Jae-Kyung Woo
In this paper, a class of multivariate matrix-exponential affine mixtures with matrix-exponential marginals is proposed. The class is shown to possess various attractive properties…
A Markov jump process associated with the matrix-exponential distribution
Oscar Peralta
Let be the density function associated to a matrix-exponential distribution of parameters . By exponentially tilting , we find a probabilistic interpretation which…
RAP-modulated Fluid Processes: First Passages and the Stationary Distribution
Nigel G. Bean, Giang T. Nguyen, Bo F. Nielsen +1
We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (R…
Wong--Zakai approximations with convergence rate for stochastic differential equations with regime switching
Giang T. Nguyen, Oscar Peralta
We construct Wong--Zakai approximations of time--inhomogeneous stochastic differential equations with regime switching (RSSDEs), and provide a convergence rate. %Given a family of…
Ruin problems for risk processes with dependent phase-type claims
Oscar Peralta, Matthieu Simon
We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is…
An explicit solution to the Skorokhod embedding problem for double exponential increments
Giang T. Nguyen, Oscar Peralta
Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In…
Strong convergence to two-dimensional alternating Brownian motion processes
Guy Latouche, Giang T. Nguyen, Oscar Peralta
Flip-flop processes refer to a family of stochastic fluid processes which converge to either a standard Brownian motion (SBM) or to a Markov modulated Brownian motion (MMBM). In re…
Rate of Strong Convergence to Markov-modulated Brownian motion
Giang T. Nguyen, Oscar Peralta
In Latouche and Nguyen (2015), the authors constructed a sequence of stochastic fluid processes and showed that it converges weakly to a Markov-modulated Brownian motion (MMBM). He…
Approximation of Ruin Probabilities via Erlangized Scale Mixtures
Oscar Peralta, Leonardo Rojas-Nandayapa, Wangyue Xie +1
In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér--Lundberg reserve process having absolutely continuous but oth…