The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

Precautionary Saving in the Small and in the Large

A new empirical study of the relation between money, nominal income, prices, and real output in postwar quarterly U.S. data rejects virtually all of the conclusions reached by Families provide individuals with risk sharing opportunities which may not otherwise be available. Within the family there is a degree of trust and a level of information which alleviates three key problems in the provision of insurance by markets open to the general public, namely, moral hazard, adverse selection, and deception. The informational advantages of pooling risk within families must be set against the inability of families to provide complete insurance because of the small size of the risk pooling group. This paper demonstrates how families can provide insurance against uncertain dates of death. Death risk sharing family arrangements effectively constitute an incomplete annuities market. Our analysis indicates that these arrangements even in small families can substitute by more than70% for complete annuities. Given the adverse selection problem and transactions costs in public annuity markets, risk pooling in families may well be preferred to purchasing market annuities. In the absence of organized public markets in annuities, these risk sharing arrangements provide powerful economic incentives for marriage and family formation. The paper suggests that inter-family transfers need have nothing to do with altruistic feelings; rather, they may simply reflect risk sharing behavior of completely selfish family members.(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of thi(This abstract was borrowed from another version of this item.)

The Family as an Incomplete Annuities Market

Apart from standard actuarial theory, this text contains methods that are relevant for actuarial practice, as well as generalised linear models with an eye on actuarial applications.

Modern Actuarial Risk Theory

Publisher Summary This chapter dealt mainly with the application of financial pricing techniques to insurance problems. However, actuarial concepts are also of increasing relevance for finance problems. This chapter presents that realistic models for asset price processes are typically incomplete. Actuarial concepts for risk-management might prove helpful in dealing with these “unhedgeable” risks. An example where such concepts are already applied, is the RAC-(risk adjusted capital) approach in insurance that has become popular among investment banks as a tool for the determination of risk capital and capital allocations. It is no coincidence that Swiss Bank Cooperation (now UBS) called one of its credit risk management systems ACRA, which stands for Actuarial Credit Risk Accounting.

Stochastic processes in insurance and finance

We consider a classical risk model and allow investment into a risky asset modelled as a Black--Scholes model as well as (proportional) reinsurance. Via the Hamilton--Jacobi--Bellman approach we find a candidate for the optimal strategy and develop a numerical procedure to solve the HJB equation. We prove a verification theorem in order to show that any increasing solution to the HJB equation is bounded and solves the optimisation problem. We prove that an increasing solution to the HJB equation exists. Finally two numerical examples are discussed.

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On minimizing the ruin probability by investment and reinsurance

Stochastic Processes for Insurance and Finance

Leshno and Levy [Leshno M, Levy H (2002) Preferred by “all” and preferred by “most” decision makers: Almost stochastic dominance. Management Sci. 48(8):1074–1085] established almost stochastic dominance to reveal preferences for most rather than all decision makers with an increasing and concave utility function. In this paper, we first provide a counterexample to the main theorem of Leshno and Levy related to almost second-degree stochastic dominance. We then redefine this dominance condition and show that the newly defined almost second-degree stochastic dominance is the necessary and sufficient condition to rank distributions for all decision makers excluding the pathological concave preferences. We further extend our results to almost higher-degree stochastic dominance. This paper was accepted by Peter Wakker, decision analysis.

Revisiting Almost Second-Degree Stochastic Dominance

This paper proposes a Conditional Value-at-Risk Minimization (CVaRM) approach to optimize an insurer’s product mix. By incorporating the natural hedging strategy of Cox and Lin (2007) and the two-factor stochastic mortality model of Cairns et al. (2006b) , we calculate an optimize product mix for insurance companies to hedge against the systematic mortality risk under parameter uncertainty. To reflect the importance of required profit, we further integrate the premium loading of systematic risk. We compare the hedging results to those using the duration match method of Wang et al. (forthcoming) , and show that the proposed CVaRM approach has a narrower quantile of loss distribution after hedging—thereby effectively reducing systematic mortality risk for life insurance companies.

On the optimal product mix in life insurance companies using conditional value at risk

INTRODUCTION Recent research has argued that alternative organizational forms will coexist in an industry because of differential relative advantages. (See, for example, Jensen and Meckling, 1976; Klein, Crawford, and Alchian, 1978; Fama and Jensen, 1983; Williamson, 1985.) The two important elements of organizational form are the ownership structure of the firm, and the degree to which the firm internalizes or outsources production, that is, the level of vertical integration. The property-liability insurance industry is characterized by firms that differ on both of these dimensions of organizational form. The range of ownership structures includes stock corporations, mutuals, and reciprocal organizations. Stockholder-owned insurers dominate the market, with 67.7 percent share of premiums written in 1994. Stock insurers controlled 55 percent of the personal lines market, which includes auto and homeowners insurance, but held a commanding lead in commercial lines, with a 79 percent share. Property-liability insurance firms also vary widely in the degree of vertical integration of the distribution system, with some firms using exclusive dealing arrangements and others contracting the sales function to independent agents who have ownership rights in the client list and who can represent a number of competing insurers. Independent agency insurers controlled 52 percent of the total market in 1994, and 71.8 percent of the commercial lines market.(1) The organizational form literature in property-liability insurance has largely treated ownership and distribution system choice separately. However, some overlap exists between the theory and empirical predictions across the ownership form and distribution system literature. For example, Mayers and Smith (1988) argue that stock insurers should be associated with a more complex mix of business than mutual insurers while Cummins and Weiss (1992), Regan and Tennyson (1996), and Regan (1997) argue that independent agency insurers should be preferred to exclusive dealers when complexity is higher. It is difficult to separate these effects empirically. An exception to treating these elements of organizational form as independent is Kim, Mayers, and Smith (1996), who argue that stock ownership and independent agency distribution are strategic complements, because independent agency is an effective device for minimizing agency costs that arise between owners and policyholders in a stock firm. Therefore, stockholder-owned insurers should choose independent agency distribution rather than exclusive dealing arrangements to minimize agency costs. While the authors of this article agree that independent agency distribution and stock ownership forms are likely to be strategic complements, the reasoning differs from that of Kim, Mayers, and Smith. An alternate explanation for the observed correlation between stock ownership form and independent agency distribution is that each of these elements offers advantages in certain lines of business and underwriting environments. In particular, the authors test the hypothesis that both stock ownership and independent agency distribution are more suited to complex lines of business and underwriting environments characterized by more risk than other combinations of ownership form and distribution system. Thus, rather than stockholder-owned firms choosing independent agency distribution, firms might first choose a business strategy, and then jointly choose ownership form and distribution system. The theory that supports this hypothesis is reviewed below. Several tests of the hypothesis are then presented. The direct correlation between ownership form and distribution system across lines of business is first measured using independence tests. Then, the authors compare the allocation of aggregate underwriting capacity to risky and complex lines of business between stock and non-stock insurers, and between independent agency and exclusive dealing insurers. …

Organizational Form in the Property-Liability Insurance Industry

While the concept of precautionary saving is well documented, that of precautionary effort has received relatively limited attention. In this note, we set up a two period model in order to analyze the conditions under which the introduction (or deterioration) of an independent background risk increases effort. INTRODUCTION Ehrlich and Becker's (1972) article initiated a very long research activity in economics around the notion of self-protection and its relationship with other risk management instruments. While many papers in economics still deal directly or indirectly on a regular basis with the topics, the discussion has spread over to other disciplines such as health management or environmental policy. Partly because of this transfer, other names for the concept of self-protection are currently used such as prevention or effort. Whatever the term adopted, self-protection activities reflect our attempt to reduce the probability of occurrence of "bad events" and these activities compete with other risk management tools such as market insurance, self-insurance, or diversification. With only one very recent exception (see below), all the economic models of self-protection are developed in a monoperiodic context (1) where the effort and its impact on the probability of a bad event are simultaneous. In a very recent paper, Menegatti (2009) has convincingly argued that while the monoperiodic model makes sense in many situations, it turns out that in other ones, a long time period may elapse between the effort and its impact on the probability of a bad event. (2) In such a context, effort becomes for the decision maker (DM) a risk management tool that competes with saving and long-term insurance. While much attention is paid to the impact of background risks in the literature devoted to insurance and saving, it is not the case for the self-protection problem. To the best of our knowledge, only Dachraoui et al. (2004) examine the impact of background risks on effort in a monoperiodic context. They conclude that the impact is ambiguous because both the marginal benefit and the marginal cost of efforts are increased by the background risk. While investments in effort are currently made to protect oneself against a specific risk that may materialize in the future, the DM also faces future risks that are beyond his control (the background risk). In this article, we analyze the impact of the presence and/or deterioration of such risks on the choice of the ex-ante level of effort. Because--as is well known--such future background risks also induce extra current savings ("precautionary savings") we use by analogy the terminology of "precautionary effort", that is, the additional effort level chosen to face the background risk. To achieve our goal, the article is organized as follows. In the next two sections, we first look at the impact of the introduction of a background risk on optimal effort and then consider the effect of a deterioration in a preexisting background risk. The section "An Extension" generalizes the previous analysis by extending the definition of the benefit of efforts along the lines developed in Jindapon and Neilson (2007). This section confirms the similarities between precautionary efforts and precautionary savings. A short conclusion summarizes the main results and indicates potential extensions. THE BASIC MODEL A DM avails upon an income [x.sub.o] that has to be allocated between current consumption and effort (e). Thanks to the effort, the DM faces in the next period a higher probability p(e) of a good outcome denoted x. With probability I - p(e), the DM receives the bad outcome x - l (l > 0) and his basic risk is thus represented by a binary random variable denoted [??]. Assuming that future utility is discounted at a rate [delta], the DM's optimization problem (3) is written: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1) in which u and p(e) are increasing and concave functions. …

Larry Y. Tzeng

Papers

Stochastic Processes for Insurance and Finance

Revisiting Almost Second-Degree Stochastic Dominance

On the optimal product mix in life insurance companies using conditional value at risk

Organizational Form in the Property-Liability Insurance Industry

Precautionary Effort: A New Look