Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach

Guambe, Calisto; Kufakunesu, Rodwell

doi:10.1080/02331934.2017.1405956

Cited by 5 publications

(6 citation statements)

References 31 publications

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“…Considering that G is a linear combination of g, we deduce that G has the same form as g in (2.33). Therefore, using the fact that ξ T ∈ L ∞ (F t ), we conclude (following Morlais [19], Royer [31] and Guambe and Kufakunesu [12]) that Equation (3.2) has a unique solution for t ∈ [0, T ].…”

Section: Forward Entropic Risk Measure and Ergodic Bsde With Jumpsmentioning

confidence: 56%

“…These assumptions imply that g is Lipschitz continuous in z and υ, a.s.. Therefore, we know from Morlais [19] (Section 3.2, Theorem 1 and 2), (see also Royer [31] and Guambe and Kufakunesu [12]) that there exists a unique solution to the BSDE (3.2) with a generator given by g in (2.33) and the risk position…”

Section: Forward Entropic Risk Measure and Ergodic Bsde With Jumpsmentioning

confidence: 99%

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An Ergodic Bsde Risk Representation in a Jump-Diffusion Framework

Guambe

Mabitsela

Kufakunesu

2021

Int. J. Theor. Appl. Finan.

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We consider the representation of forward entropic risk measures using the theory of ergodic backward stochastic differential equations in a jump-diffusion framework. Our paper can be viewed as an extension of the work considered by Chong et al. (2019) in the diffusion case. We also study the behavior of a forward entropic risk measure under jumps when a financial position is held for a longer maturity.

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Section: Forward Entropic Risk Measure and Ergodic Bsde With Jumpsmentioning

confidence: 56%

Section: Forward Entropic Risk Measure and Ergodic Bsde With Jumpsmentioning

confidence: 99%

An Ergodic Bsde Risk Representation in a Jump-Diffusion Framework

Guambe

Mabitsela

Kufakunesu

2021

Int. J. Theor. Appl. Finan.

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“…They derived the HJB equation by applying the dynamic programming principle and found closed-form solutions. (Guambe & Kufakunesu, 2018) explored optimal investment, consumption and insurance problems. They considered a market with a real zero-coupon bond, the inflation-linked real money account and a risky share following a jump-diffusion process.…”

Section: Links To the Literaturementioning

confidence: 99%

Optimal Investment, Consumption and Life Insurance Problem with Stochastic Environments

Jere¹,

Offen²,

Basmanebothe³

2022

JMR

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Optimal investment, consumption and life insurance problem with stochastic environments for a CRRA wage-earner is solved in this study.  The wage-earner invests in the financial market with one risk-free security, one risky security, receives labor income and has a life insurance policy in the insurance market. A life insurance policy is purchased to hedge the financial wealth for the beneficiary in case of wage earner premature death. The interest rate and the volatility are stochastic. The stochastic interest rate dynamics of risk-free security follow a Ho-Lee model and the risky security follow Heston’s model with stochastic volatility parameter dynamics following a Cox-Ingersoll-Ross (CIR) model. The objective of the wage-earner is to allocate wealth between risky security and risk-free security but also buy a life insurance policy during the investment period to maximize the expected discounted utilities derived from consumption, legacy and terminal wealth over an uncertain lifetime. By applying Bellman's optimality principle, the associated HJB PDE for the value function is established. The power utility function is employed for our analysis to obtain the value function and optimal policies. Finally, numerical examples and simulations are provided.

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“…We introduce a version of a maximum principle approach for stochastic volatility model under diffusion with partial information, which is mainly based on the results in Guambe and Kufakunesu [14]. On a complete filtered probability space (Ω, F , {F t } t∈[0,T ] , P), suppose that the dynamics of the state process is given by the following stochastic differential equation (SDE)…”

Section: Appendixmentioning

confidence: 99%

Optimal asset allocation for a DC plan with partial information under inflation and mortality risks

Guambe¹,

Kufakunesu²,

Zyl³

et al. 2018

Preprint

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We study an asset allocation stochastic problem with restriction for a definedcontribution pension plan during the accumulation phase. We consider a financial market with stochastic interest rate, composed of a risk-free asset, a real zero coupon bond price, the inflation-linked bond and the risky asset. A plan member aims to maximize the expected power utility derived from the terminal wealth. In order to protect the rights of a member who dies before retirement, we introduce a clause which allows to withdraw his premiums and the difference is distributed among the survival members. Besides the mortality risk, the fund manager takes into account the salary and the inflation risks. We then obtain closed form solutions for the asset allocation problem using a sufficient maximum principle approach for the problem with partial information. Finally, we give a numerical example

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Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach

Cited by 5 publications

References 31 publications

An Ergodic Bsde Risk Representation in a Jump-Diffusion Framework

An Ergodic Bsde Risk Representation in a Jump-Diffusion Framework

Optimal Investment, Consumption and Life Insurance Problem with Stochastic Environments

Optimal asset allocation for a DC plan with partial information under inflation and mortality risks

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