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Moral Hazard and Insurance: Optimality, Risk and Preferences

Sundström, Kristian LU (2004)
Abstract (Swedish)
Popular Abstract in Swedish

Försäkringsmarknader präglas generellt av informationsproblem av olika slag. I denna avhandling studeras ett specifikt sådant problem: moral hazard. Detta innebär att den försäkrade kan vidta försiktighetsåtgärder för att minska sannolikheten för att drabbas av en olycka, men att försäkringsbolaget inte säkert kan urskilja storleken på dessa försiktighetsåtgärder. Vi får därför en lösning som från den försäkrades sida är icke-optimal, då han inte kan erbjudas full försäkring, vilket han normalt vill ha. Avhandlingen består av tre olika delar. Den första studerar fallet där informationen är perfekt, det vill säga där nivån på försiktighetsåtgärder är möjlig att verifiera för försäkringsbolaget.... (More)
Popular Abstract in Swedish

Försäkringsmarknader präglas generellt av informationsproblem av olika slag. I denna avhandling studeras ett specifikt sådant problem: moral hazard. Detta innebär att den försäkrade kan vidta försiktighetsåtgärder för att minska sannolikheten för att drabbas av en olycka, men att försäkringsbolaget inte säkert kan urskilja storleken på dessa försiktighetsåtgärder. Vi får därför en lösning som från den försäkrades sida är icke-optimal, då han inte kan erbjudas full försäkring, vilket han normalt vill ha. Avhandlingen består av tre olika delar. Den första studerar fallet där informationen är perfekt, det vill säga där nivån på försiktighetsåtgärder är möjlig att verifiera för försäkringsbolaget. Genom att förenkla tidigare modeller identifierar vi två inneboende svagheter i dessa. Dels går det inte att uppfylla villkoren för att prisjämvikt ska kunna erhållas, dels är risknivå och nytta positivt korrelerade. Det senare resultatet innebär att vi kan höja risken i ekonomin och samtidigt höja försäkringstagarens nytta, vilket inte är intuitivt eftersom dessa antas ogilla risk I den andra delen av avhandlingen införs antagandet att nivån på försiktighetsåtgärder inte kan verifieras av försäkringsbolaget. Detta medför många svårigheter, både tolkningsmässigt och beräkningsmässigt. Vi visar att våra antaganden förenklar beräkningen, och att det är möjligt, givet vissa ytterligare antaganden, att finna optimala och unika lösningar till problemet. Detta resultat förenklar vidare analyser inom området. I den sista delen inför vi antagandet att risknivån påverkar sannolikheten för en olycka. Detta antagande innebär att det är dyrare att förhindra en stor potentiell olycka (översvämning) än en liten (cykelstöld). Med detta enkla antagande kan vi visa att båda problemen som uppstår med den ursprungliga modellen försvinner. Det går alltså nu att uppfylla villkoren för en prisjämvikt under rimliga antaganden, och förhållandet mellan risk och nytta ändras så att en högre risk alltid är sämre än en låg risk för försäkringstagaren, allt annat lika. (Less)
Abstract
The thesis consists of an introductory chapter, followed by three chapters which all deal with theoretical issues related to moral hazard and insurance. In Chapter 2 we assume symmetric and perfect information. We conclude that, given some standard assumptions, the expected utility function cannot be quasi-concave, which strengthens earlier findings in the literature. As a consequence convex preferences cannot be obtained, a fact that has far-reaching negative consequences for, among other things, the existence of a price equilibrium. A second result concerns the relation between risk and utility in traditionally employed models of moral hazard and insurance. We use the envelope concept to conclude that it is possible to increase the... (More)
The thesis consists of an introductory chapter, followed by three chapters which all deal with theoretical issues related to moral hazard and insurance. In Chapter 2 we assume symmetric and perfect information. We conclude that, given some standard assumptions, the expected utility function cannot be quasi-concave, which strengthens earlier findings in the literature. As a consequence convex preferences cannot be obtained, a fact that has far-reaching negative consequences for, among other things, the existence of a price equilibrium. A second result concerns the relation between risk and utility in traditionally employed models of moral hazard and insurance. We use the envelope concept to conclude that it is possible to increase the expected utility of an agent by increasing his exposure to risk, while holding fixed all other relevant variables of the model. Since the agents are assumed to be risk averse, this result is counter-intuitive and requires further clarification. Chapter 3 introduces asymmetric information, which implies that the behaviour of the insured cannot be observed. Our assumptions, which are different from those made earlier in the literature, are shown to be sufficient to validate the first-order approach, which means that the first order condition of the consumer problem can replace the incentive compatibility constraint, making the problem much more mathematically tractable. In the second part of the chapter we use basic differential geometry to conclude two existence and uniqueness results, concerning the relation between optimal contracts and the economy under asymmetric information. These results are made under the assumption of constant absolute risk aversion. In Chapter 4 we introduce an alternative prevention technology, describing the relation between precautionary effort and probability of an accident. The main argument is that a big risk (for example a flood) should be more expensive to prevent than a small risk (for example a bicycle theft). We thus include the risk level as a determinant of the probability of an accident. In turn, we use this new prevention technology to analyse the problems advanced in Chapter 2. Among other things, we find that it is now, indeed, possible to obtain convex preferences under reasonable assumptions, a result which has not been presented previously in the literature. Since many of the problems of moral hazard, as discussed in the introductory section, relates to non-convex preferences, this finding should be considered one of the most interesting results of the entire dissertation. In addition, we also analyse the implications of introducing the new probability function upon the relation between risk and expected utility. We conduct an analysis similar to the one carried out in Chapter 2, and conclude that the counter-intuitive result found in that chapter has now disappeared. Thus a higher risk always induces a lower utility, a result we find to be more consistent with intuition. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Balasko, Yves, University of York
organization
publishing date
type
Thesis
publication status
published
subject
keywords
asymmetric information, second best solution, first best solution, Insurance, Moral Hazard
defense location
EC3:211
defense date
2004-11-19 14:15
language
English
LU publication?
yes
id
d07575ef-6847-42c5-8ff7-f26ed6e1c407 (old id 1779656)
date added to LUP
2011-02-02 11:22:26
date last changed
2016-09-19 08:45:19
@phdthesis{d07575ef-6847-42c5-8ff7-f26ed6e1c407,
  abstract     = {The thesis consists of an introductory chapter, followed by three chapters which all deal with theoretical issues related to moral hazard and insurance. In Chapter 2 we assume symmetric and perfect information. We conclude that, given some standard assumptions, the expected utility function cannot be quasi-concave, which strengthens earlier findings in the literature. As a consequence convex preferences cannot be obtained, a fact that has far-reaching negative consequences for, among other things, the existence of a price equilibrium. A second result concerns the relation between risk and utility in traditionally employed models of moral hazard and insurance. We use the envelope concept to conclude that it is possible to increase the expected utility of an agent by increasing his exposure to risk, while holding fixed all other relevant variables of the model. Since the agents are assumed to be risk averse, this result is counter-intuitive and requires further clarification. Chapter 3 introduces asymmetric information, which implies that the behaviour of the insured cannot be observed. Our assumptions, which are different from those made earlier in the literature, are shown to be sufficient to validate the first-order approach, which means that the first order condition of the consumer problem can replace the incentive compatibility constraint, making the problem much more mathematically tractable. In the second part of the chapter we use basic differential geometry to conclude two existence and uniqueness results, concerning the relation between optimal contracts and the economy under asymmetric information. These results are made under the assumption of constant absolute risk aversion. In Chapter 4 we introduce an alternative prevention technology, describing the relation between precautionary effort and probability of an accident. The main argument is that a big risk (for example a flood) should be more expensive to prevent than a small risk (for example a bicycle theft). We thus include the risk level as a determinant of the probability of an accident. In turn, we use this new prevention technology to analyse the problems advanced in Chapter 2. Among other things, we find that it is now, indeed, possible to obtain convex preferences under reasonable assumptions, a result which has not been presented previously in the literature. Since many of the problems of moral hazard, as discussed in the introductory section, relates to non-convex preferences, this finding should be considered one of the most interesting results of the entire dissertation. In addition, we also analyse the implications of introducing the new probability function upon the relation between risk and expected utility. We conduct an analysis similar to the one carried out in Chapter 2, and conclude that the counter-intuitive result found in that chapter has now disappeared. Thus a higher risk always induces a lower utility, a result we find to be more consistent with intuition.},
  author       = {Sundström, Kristian},
  keyword      = {asymmetric information,second best solution,first best solution,Insurance,Moral Hazard},
  language     = {eng},
  school       = {Lund University},
  title        = {Moral Hazard and Insurance: Optimality, Risk and Preferences},
  year         = {2004},
}