Optimal Investment for a Defined-Contribution Pension Scheme Under a Regime Switching Model

Chen, An; Delong, Łukasz

doi:10.2139/ssrn.2447345

Cited by 8 publications

(9 citation statements)

References 23 publications

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“…To express the dependence of the matrix Q given by (8) on α in the present section, we write Q α (so Q α = A ⊗ diag(λ) + I ⊗ αQ) and F α (t) instead of F (t) as given in Lemma 2.5.…”

Section: Rapid Switchingmentioning

confidence: 99%

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Explicit Computations for Some Markov Modulated Counting Processes

Mandjes

Spreij

2016

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In finance, for instance, one could identify the background process with the 'state of the economy', to which asset prices react, or as an identification of the varying default rate of an obligor. The key feature of the counting processes in this paper is that their intensity processes are functions of a finite state Markov chain. This kind of processes can be used to model default events of some companies.Many quantities of interest in this paper, like conditional characteristic functions, can all be derived from conditional probabilities, which can, in principle, be analytically computed. We will also study limit results for models with rapid switching, which occur when inflating the intensity matrix of the Markov chain by a factor tending to infinity. The paper is largely expository in nature, with a didactic flavor.

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Section: Rapid Switchingmentioning

confidence: 99%

“…Various specific models have been considered since then, see for instance [1,11,12]. For other direct applications of models with regime switching in finance (hedging of claims, interest rate models, credit risk, application to pension funds) we refer to [8,22,23,30,31] for recent results.…”

Section: Introductionmentioning

confidence: 99%

Explicit Computations for Some Markov Modulated Counting Processes

Mandjes

Spreij

2016

Springer Proceedings in Mathematics &Amp; Statistics

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“…In these models, the studied processes are assumed to have several "regimes", with their own regime specific parameters and rules for regime switching. For a more detailed literature review on the uses of regime-switching models in insurance and finance, see Liu et al (2011), Shen and Siu (2013), Freeman (2013), Fan et al (2015), Siu et al (2015), Chen and Delong (2015), Rambeerich and Pantelous (2016) and references therein.…”

Section: Motivation: Stability Feedback Control and H ∞ Controlmentioning

confidence: 99%

Robust Stability, Stabilisation and H-Infinity Control for Premium-Reserve Models in a Markovian Regime Switching Discrete-Time Framework

2016

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The premium pricing process and the medium- and long-term stability of the reserve policy under conditions of uncertainty present very challenging issues in relation to the insurance world. Over the last two decades, applications of Markovian regime switching models to finance and macroeconomics have received strong attention from researchers, and particularly market practitioners. However, relatively little research has so far been carried out in relation to insurance. This paper attempts to consider how a linear Markovian regime switching system in discrete-time could be applied to model the medium- and long-term reserves and the premiums (abbreviated here as the P-R process) for an insurer. Some recently developed techniques from linear robust control theory are applied to explore the stability, stabilisation and robust H∞-control of a P-R system, and the potential effects of abrupt structural changes in the economic fundamentals, as well as the insurer's strategy over a finite time period. Sufficient linear matrix inequality conditions are derived for solving the proposed sub-problems. Finally, a numerical example is presented to illustrate the applicability of the theoretical results.

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“…Numerous regime-switching models have been proposed and investigated recently, see, e.g., Cheng and Zhan (2020), Jin et al (2020), Shen et al (2019), Cao et al (2018), Liu and Privault (2018), Ignatieva et al (2018), Xu et al (2017), Wang et al (2016), Landriault et al (2015), Chen and Delong (2015), Chen et al (2014), Guillou et al (2013), Asmussen and Albrecher (2010), Kim and Kim (2007), Lu (2006), Bäuerle (1996), Asmussen (1989) and Reinhard (1984). Some useful suggestions and justifications for the application of Markov switching models in insurance mathematics can also be found in Rabehasaina (2009), De ¸bicka (2013) and D'Amico (2014).…”

Section: Introductionmentioning

confidence: 99%

Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model

Gajek

Rudź

2020

Methodol Comput Appl Probab

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Insolvency risk measures play important role in the theory and practice of risk management. In this paper, we provide a numerical procedure to compute vectors of their exact values and prove for them new upper and/or lower bounds which are shown to be attainable. More precisely, we investigate a general insolvency risk measure for a regime-switching Sparre Andersen model in which the distributions of claims and/or wait times are driven by a Markov chain. The measure is defined as an arbitrary increasing function of the conditional expected harm of the deficit at ruin, given the initial state of the Markov chain. A vector-valued operator L, generated by the regime-switching process, is introduced and investigated. We show a close connection between the iterations of L and the risk measure in a finite horizon. The approach assumed in the paper enables to treat in a unified way several discrete and continuous time risk models as well as a variety of important vector-valued insolvency risk measures.

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Optimal Investment for a Defined-Contribution Pension Scheme Under a Regime Switching Model

Cited by 8 publications

References 23 publications

Explicit Computations for Some Markov Modulated Counting Processes

Explicit Computations for Some Markov Modulated Counting Processes

Robust Stability, Stabilisation and H-Infinity Control for Premium-Reserve Models in a Markovian Regime Switching Discrete-Time Framework

Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model

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