Related papers: Two-dimensional forward and backward transition ra…
The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial…
Recent literature has found conditional transition rates to be a useful tool for avoiding Markov assumptions in multi-state models. While the estimation of univariate conditional transition rates has been extensively studied, the…
The main purpose of this work is to derive a partial differential equation for the reserves of life insurance liabilities subject to stochastic interest rates where the benefits and premiums depend directly on changes in the interest rate…
A multi--state life insurance model is naturally described in terms of the intensity matrix of an underlying (time--inhomogeneous) Markov process which describes the dynamics for the states of an insured person. Between and at transitions,…
Reversible computing is a new paradigm that has emerged recently and extends the traditional forwards-only computing mode with the ability to execute in backwards, so that computation can run in reverse as easily as in forward. Two…
It is well-known that combining life annuities and death benefits introduce opposite effects in payments with respect to the mortality risk on the lifetime of the insured. In a general multi-state framework with multiple product types, such…
We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth and death like transitions, for which it is shown that for any state $i$, the rate of two…
We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of…
In this paper, we demonstrate through the use of matrix calculus a transparent analysis of fractional inhomogeneous Markov models for life insurance where transition matrices commute. The resulting formulae are intuitive matrix…
The purpose of the present paper is to incorporate stochastic interest rates into a matrix-approach to multi-state life insurance, where formulas for reserves, moments of future payments and equivalence premiums can be obtained as explicit…
This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous.…
In this paper we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial…
The notion of a credit spread curve is fundamental in fixed income investing, but in practice it is not `given' and needs to be constructed from bond prices either for a particular issuer, or for a sector rating-by-rating. Rather than…
A method yielding simple relationships among bilateral birth-and-death processes is outlined. This allows one to relate birth and death rates of two processes in such a way that their transition probabilities, first-passage-time densities…
The calculation of the insurance liabilities of a cohort of dependent individuals in general requires the solution of a high-dimensional system of coupled linear forward integro-differential equations, which is infeasible for a larger…
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes…
For many stochastic dynamic systems, the Mean First Passage Time (MFPT) is a useful concept, which gives expected time before a state of interest. This work is an extension of MFPT in several ways. (1) We show that for some systems the…
This paper develops a continuous-time filtering framework for estimating a hazard rate subject to an unobservable change-point. This framework naturally arises in both financial and insurance applications, where the default intensity of a…
In modern life insurance, Markov processes in continuous time on a finite or at least countable state space have been over the years an important tool for the modelling of the states of an insured. Motivated by applications in disability…
Rate change calculations in the literature involve deterministic methods that measure the change in premium for a given policy. The definition of rate change as a statistical parameter is proposed to address the stochastic nature of the…