Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

Kasumo, Christian

doi:10.3390/mca24010021

Cited by 4 publications

(3 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore it is important to secure expensive property and insurance provides that security. In [1], Kasumo observed that the provision of insurance requires competent management as poor management may lead to the eventual ruin of the insurance company, resulting in its failure to fulfill its obligations. This happens when the insurer's surplus level falls below zero, thus making the company bankrupt.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Insurance Companies Portfolio Optimization with Possibilities of Recovery after Ruin: A Case of Exponential Utility Function

Komunte¹,

Kasumo²,

Masanja³

2021

JMI

View full text Add to dashboard Cite

In this paper, we propose and analyze the perturbed mathematical model for modeling the portfolio of insurance companies with possibilities of recovery after ruin. Return on investment and refinancing are used as approaches for overcoming ruin. The model is analyzed for different cases of possibilities of recovery after ruin within [0, 1]. The results indicate that the return on investment plays an important role in reducing the ultimate ruin and that as the possibility of recovery for insurance companies increases the return on investment reduces the ruin at a fast rate. Finally, the study recommends that all insurance companies should have well trained staff in risk management who can study the company’s portfolio and gives suggestions to managers on how to avoid or minimize ruin and how to recover in case ruin occurs.

show abstract

Section: Introductionmentioning

confidence: 99%

“…A vast number of researchers have studied this classical risk process perturbed by diffusion in the insurance industry, some of them being [1,4,11,12,13,14].…”

mentioning

confidence: 99%

Insurance Companies Portfolio Optimization with Possibilities of Recovery after Ruin: A Case of Exponential Utility Function

Komunte¹,

Kasumo²,

Masanja³

2021

JMI

View full text Add to dashboard Cite

show abstract

“…Since the generalized Lundberg equation may have multiple positive roots, Bergel corresponds the obtained roots to the solutions of the differential equations one-by-one, taking into account factors such as dividends [26]. Kasumo used a block-by-block method to calculate the bankruptcy probability including the investment returns of the standard Black-Scholes model, illustrating the sensitivity of the ruin probability to stock price fluctuations [27].…”

Section: Introductionmentioning

confidence: 99%

Solution of Ruin Probability for Continuous Time Model Based on Block Trigonometric Exponential Neural Network

et al. 2020

View full text Add to dashboard Cite

The ruin probability is used to determine the overall operating risk of an insurance company. Modeling risks through the characteristics of the historical data of an insurance business, such as premium income, dividends and reinvestments, can usually produce an integral differential equation that is satisfied by the ruin probability. However, the distribution function of the claim inter-arrival times is more complicated, which makes it difficult to find an analytical solution of the ruin probability. Therefore, based on the principles of artificial intelligence and machine learning, we propose a novel numerical method for solving the ruin probability equation. The initial asset u is used as the input vector and the ruin probability as the only output. A trigonometric exponential function is proposed as the projection mapping in the hidden layer, then a block trigonometric exponential neural network (BTENN) model with a symmetrical structure is established. Trial solution is set to meet the initial value condition, simultaneously, connection weights are optimized by solving a linear system using the extreme learning machine (ELM) algorithm. Three numerical experiments were carried out by Python. The results show that the BTENN model can obtain the approximate solution of the ruin probability under the classical risk model and the Erlang(2) risk model at any time point. Comparing with existing methods such as Legendre neural networks (LNN) and trigonometric neural networks (TNN), the proposed BTENN model has a higher stability and lower deviation, which proves that it is feasible and superior to use a BTENN model to estimate the ruin probability.

show abstract

Reducing the Possibility of Ruin by Maximizing the Survival Function for the Insurance Company’s Portfolio

Masanja

2022

Journal of Mathematics

View full text Add to dashboard Cite

In this paper, the intention was to reduce the possibility of ruin in the insurance company by maximizing its survival function. This paper uses a perturbed classical risk process as the basic model. The basic model was later compounded by refinancing and return on investment. The Hamilton–Jacobi–Bellman equation and integro-differential equation of Volterra type were obtained. The Volterra integro-differential equation for the survival function of the insurance company was converted to a third-order ordinary differential equation which was later converted into a system of first-order ordinary differential equations. This system was then solved numerically using the fourth-order Runge-Kutta method. The results show that the survival function increases with the increase in the intensity of the counting process but decreases with an increase in the instantaneous rate of stock return and return volatility. This is due to the fact that the insurance company faces more risk. Thus, this paper suggests that in this situation, more investments should be made in risk-free assets.

show abstract

Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

Cited by 4 publications

References 47 publications

Insurance Companies Portfolio Optimization with Possibilities of Recovery after Ruin: A Case of Exponential Utility Function

Insurance Companies Portfolio Optimization with Possibilities of Recovery after Ruin: A Case of Exponential Utility Function

Solution of Ruin Probability for Continuous Time Model Based on Block Trigonometric Exponential Neural Network

Reducing the Possibility of Ruin by Maximizing the Survival Function for the Insurance Company’s Portfolio

Contact Info

Product

Resources

About