Expanding insurability through exploiting linear partial information

Peter Zweifel; Peter Zweifel

doi:10.3934/DSFE.2022001

Data Science in Finance and Economics

2022, Volume 2, Issue 1: 1-16. doi: 10.3934/DSFE.2022001

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Research article

Expanding insurability through exploiting linear partial information

Peter Zweifel ^,

Emeritus, Socioeconomic Institute, University of Zurich, Switzerland

Received: 11 February 2022 Revised: 11 March 2022 Accepted: 17 March 2022 Published: 23 March 2022
JEL Codes: C14, C44, C72, D81, D83, G11, G17, G22, G34

This contribution aims to expand insurability using partial linear information (LPI) on probabilities of the type, $ {r}_{1}\ge {r}_{3} $ (with $ {r}_{1}+{r}_{2}+{r}_{3}+\dots {r}_{n} = {1} $). LPI theory permits to exploit such weak information for systematic decision-making provided the decision-maker is willing to apply the maxEmin criterion in a game against Nature. The maxEmin rule is a natural generalization of expected profit (probabilities are known) and the maximin rule (probabilities are unknown). LPI theory is used to find out whether a crypto assets portfolio offered to an insurance company is insurable. In an example, an unfavorable future development of losses causes maximum expected loss to exceed the present value of premiums, rendering the portfolio uninsurable according to maxEmin. However, this changes when LPI concerning this development is available, while the integration of uncertain returns from investing the extra premium fails to achieve insurability in this example. Evidently, LPI theory enables insurers to accept risks that otherwise are deemed uninsurable.
- insurability,
- linear partial information,
- LPI theory,
- maxEmin criterion
Citation: Peter Zweifel. Expanding insurability through exploiting linear partial information[J]. Data Science in Finance and Economics, 2022, 2(1): 1-16. doi: 10.3934/DSFE.2022001

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Abstract

This contribution aims to expand insurability using partial linear information (LPI) on probabilities of the type, $ {r}_{1}\ge {r}_{3} $ (with $ {r}_{1}+{r}_{2}+{r}_{3}+\dots {r}_{n} = {1} $). LPI theory permits to exploit such weak information for systematic decision-making provided the decision-maker is willing to apply the maxEmin criterion in a game against Nature. The maxEmin rule is a natural generalization of expected profit (probabilities are known) and the maximin rule (probabilities are unknown). LPI theory is used to find out whether a crypto assets portfolio offered to an insurance company is insurable. In an example, an unfavorable future development of losses causes maximum expected loss to exceed the present value of premiums, rendering the portfolio uninsurable according to maxEmin. However, this changes when LPI concerning this development is available, while the integration of uncertain returns from investing the extra premium fails to achieve insurability in this example. Evidently, LPI theory enables insurers to accept risks that otherwise are deemed uninsurable.

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