Optimal control of investment, premium and deductible for a non-life insurance company

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Optimal control of investment, premium and deductible for a non-life insurance company. / Christensen, Bent Jesper; Parra-Alvarez, Juan Carlos; Serrano, Rafael.

Aarhus : Institut for Økonomi, Aarhus Universitet, 2020.

Research output: Working paperResearch

Harvard

APA

Christensen, B. J., Parra-Alvarez, J. C., & Serrano, R. (2020). Optimal control of investment, premium and deductible for a non-life insurance company. Institut for Økonomi, Aarhus Universitet. CREATES Research Papers, No. 2020-11

CBE

MLA

Christensen, Bent Jesper, Juan Carlos Parra-Alvarez and Rafael Serrano Optimal control of investment, premium and deductible for a non-life insurance company. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal number 2020-11). 2020., 40 p.

Vancouver

Author

Christensen, Bent Jesper ; Parra-Alvarez, Juan Carlos ; Serrano, Rafael. / Optimal control of investment, premium and deductible for a non-life insurance company. Aarhus : Institut for Økonomi, Aarhus Universitet, 2020. (CREATES Research Papers; No. 2020-11).

Bibtex

@techreport{6548b5b6087846ceb04639056c14bdd7,
title = "Optimal control of investment, premium and deductible for a non-life insurance company",
abstract = "A risk-averse insurance company controls its reserve, modelled as a perturbed Cram{\'e}r-Lundberg process, by choice of both the premium p and the deductible K offered to potential customers. The surplus is allocated to financial investment in a riskless and a basket of risky assets potentially correlating with the insurance risks and thus serving as a partial hedge against these. Assuming customers differ in riskiness, increasing p or K reduces the number of customers n(p,K) and increases the arrival rate of claims per customer λ(p,K) through adverse selection, with a combined negative effect on the aggregate arrival rate n(p,K)λ(p,K). We derive the optimal premium rate, deductible, investment strategy, and dividend payout rate (consumption by the owner-manager) maximizing expected discounted life-time utility of intermediate consumption under the assumption of constant absolute risk aversion. Closed-form solutions are provided under specific assumptions on the distributions of size and frequency claims.",
keywords = "Stochastic optimal control, Hamilton-Jacobi-Bellman equation, Jump-diffusion, Adverse selection, Premium control, Deductible control, Optimal investment strategy",
author = "Christensen, {Bent Jesper} and Parra-Alvarez, {Juan Carlos} and Rafael Serrano",
year = "2020",
month = oct,
language = "English",
series = "CREATES Research Papers",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
number = "2020-11",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - Optimal control of investment, premium and deductible for a non-life insurance company

AU - Christensen, Bent Jesper

AU - Parra-Alvarez, Juan Carlos

AU - Serrano, Rafael

PY - 2020/10

Y1 - 2020/10

N2 - A risk-averse insurance company controls its reserve, modelled as a perturbed Cramér-Lundberg process, by choice of both the premium p and the deductible K offered to potential customers. The surplus is allocated to financial investment in a riskless and a basket of risky assets potentially correlating with the insurance risks and thus serving as a partial hedge against these. Assuming customers differ in riskiness, increasing p or K reduces the number of customers n(p,K) and increases the arrival rate of claims per customer λ(p,K) through adverse selection, with a combined negative effect on the aggregate arrival rate n(p,K)λ(p,K). We derive the optimal premium rate, deductible, investment strategy, and dividend payout rate (consumption by the owner-manager) maximizing expected discounted life-time utility of intermediate consumption under the assumption of constant absolute risk aversion. Closed-form solutions are provided under specific assumptions on the distributions of size and frequency claims.

AB - A risk-averse insurance company controls its reserve, modelled as a perturbed Cramér-Lundberg process, by choice of both the premium p and the deductible K offered to potential customers. The surplus is allocated to financial investment in a riskless and a basket of risky assets potentially correlating with the insurance risks and thus serving as a partial hedge against these. Assuming customers differ in riskiness, increasing p or K reduces the number of customers n(p,K) and increases the arrival rate of claims per customer λ(p,K) through adverse selection, with a combined negative effect on the aggregate arrival rate n(p,K)λ(p,K). We derive the optimal premium rate, deductible, investment strategy, and dividend payout rate (consumption by the owner-manager) maximizing expected discounted life-time utility of intermediate consumption under the assumption of constant absolute risk aversion. Closed-form solutions are provided under specific assumptions on the distributions of size and frequency claims.

KW - Stochastic optimal control

KW - Hamilton-Jacobi-Bellman equation

KW - Jump-diffusion

KW - Adverse selection

KW - Premium control

KW - Deductible control

KW - Optimal investment strategy

M3 - Working paper

T3 - CREATES Research Papers

BT - Optimal control of investment, premium and deductible for a non-life insurance company

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -