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Valuation of finance/insurance contracts: Efficient hedging and stochastic interest rates modeling

Research paper by Alexander Melnikov, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-;mails: {melnikov, stong2}@ualberta.ca<br>Shuo Tong, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-;mails: {melnikov, stong2}@ualberta.ca

Indexed on: 13 May '16Published on: 18 Apr '14Published in: Risk and Decision Analysis



Abstract

This paper studies the problem of hedging equity-linked life insurance contracts with efficient hedging technique in stochastic interest economy. In our setting, the payoff of life insurance contracts is based on two risky assets, where the return processes are driven by different correlated Wiener processes. The stochastic interest rate is assumed to follow the Heath–Jarrow–Morton framework. We obtain explicit formulas for both the price of a single premium contract and the corresponding survival probability. Moreover, a numerical example illustrates how this efficient hedging technique is applied to manage the balance between financial and insurance risks for a risk-taking insurance company. Content Type Journal ArticlePages 23-41DOI 10.3233/RDA-130099Authors Alexander Melnikov, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.caShuo Tong, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.ca Journal Risk and Decision AnalysisOnline ISSN 1875-9173Print ISSN 1569-7371 Journal Volume Volume 5 Journal Issue Volume 5, Number 1 / 2014 This paper studies the problem of hedging equity-linked life insurance contracts with efficient hedging technique in stochastic interest economy. In our setting, the payoff of life insurance contracts is based on two risky assets, where the return processes are driven by different correlated Wiener processes. The stochastic interest rate is assumed to follow the Heath–Jarrow–Morton framework. We obtain explicit formulas for both the price of a single premium contract and the corresponding survival probability. Moreover, a numerical example illustrates how this efficient hedging technique is applied to manage the balance between financial and insurance risks for a risk-taking insurance company. Content Type Journal ArticlePages 23-41DOI 10.3233/RDA-130099Authors Alexander Melnikov, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.caShuo Tong, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.ca Content Type Journal ArticleContent Type Journal ArticlePages 23-41DOI 10.3233/RDA-130099Authors Alexander Melnikov, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.caShuo Tong, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.ca Authors Alexander Melnikov, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.caShuo Tong, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.ca Alexander Melnikov, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.caShuo Tong, Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada. E-mails: {melnikov, stong2}@ualberta.ca Journal Risk and Decision AnalysisOnline ISSN 1875-9173Print ISSN 1569-7371 Journal Volume Volume 5 Journal Issue Volume 5, Number 1 / 2014 Journal Risk and Decision AnalysisOnline ISSN 1875-9173Print ISSN 1569-7371 Journal Risk and Decision AnalysisJournal Risk and Decision AnalysisRisk and Decision AnalysisOnline ISSN 1875-9173Online ISSN 1875-9173Print ISSN 1569-7371Print ISSN 1569-7371 Journal Volume Volume 5 Journal Volume Volume 5Journal Volume Volume 5 Journal Issue Volume 5, Number 1 / 2014 Journal Issue Volume 5, Number 1 / 2014Journal Issue Volume 5, Number 1 / 2014Volume 5, Number 1 / 2014

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