Game Theory in Life Insurance
The insurance industry has long been applying game theory to evaluate whether or not individuals are insurable and determine how much premium to charge them based on their apparent needs. This interaction between the consumer and the insurance company can be characterized as a game because not only are they playing against one another but each party is waging on an outcome more beneficial to them. In a traditional life insurance, there are many variables to consider when utilizing game theory to form a strategy as there are investment components along with complex riders. Thus, in order to keep the game relatively simple, this paper will assume the insurance being considered is term life and use game
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Instead, the presumed opponent is Mother Nature. Professor Marvin D. Troutt, who wrote the classic work on game theoretical approaches to life insurance purchasing, explains how the potential consumer is at odds with nature: “there is the option of delaying the purchase for a number of years in the future at the risk that Nature, or chance, will intervene and allow death (or insurability) to occur before insurance begins” (Troutt, 1988).
Using Troutt’s model in a normal-form matrix below, the buyer has two possible strategies (Insure and Not Insure) while Mother Nature has two possible strategies (Live and Die). The payoff of the game is the family’s wealth at the end of the year. The payoff matrix looks like this:
Mother Nature
Strategy
Live
Die
Buyer
Insure
-1, 0
1, 0
Not Insure
0, 0
-1, 0
Figure 1
As the above table is dealing with one’s life, it is safe to assume that the game is a one-shot, simultaneous game for the fact that this game is only going to happen once and that the decision of each player is unknown from the other. In this scenario, the prospective buyer’s best strategy (1, 0) for this game is to ‘Insure’ if Mother Nature chooses ‘Die’ as highlighted above. This is ideal for the buyer because this unfortunate incident will generate a payoff to benefit the family based on the face amount purchased. Two of the
1- A local real estate investor in Orlando is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:
In life we are filled with many decisions, some may be abrupt while others are calculated. Making the right decision is the most challenging thing that we may ever be compelled to undertake in life. Psychology tells us that decision-making is the process of analyzing and deciding alternatives based strictly on beliefs, values, and preferences of the decision-maker. Our decisions are consequently what dictates our types of living conditions and can expand as far as determining our own health or the health of our families. In Lorraine Hansberry’s story A Raisin In The Sun the fictional character from the book, Mama, decides to use the insurance money she received from the loss of her husband to move out of her current neighborhood to move
Thomas, C. R., & Maurice, S. C. (2010). Managerial Economics: Foundations of Business Analysis and Strategy (10th ed.). New York:
However, our game was not based on these so called rational choices. Instead, we looked at what would benefit us the best. Or perhaps we considered who our opponent was and adjusted our strategy accordingly. Game Theory does not provide explanations for these variables. It would be interesting to see if one could create a mathematical scheme that could include such variables as “irrationality” and relationships.
Parnell, J. A. (2014). Strategic management: Theory and practice (4th ed.). Los Angeles, CA: SAGE.
Life insurance is important but we face two problems, first we don’t know when we are going to die and then the possibility of dying to soon. Dying before we are able to secure financial security for love ones. Life insurance protects our love ones from the death of you or spouse. This is especially important for the one who brings the higher income (breadwinner). If only one person earns income and other people rely on that income, we need to make sure those people are still being taken care after an
Based on Dworkin’s view of distributive equality, people should be compensated materially if they suffer in the outcome of bad brute luck because having bad brute luck is out of their control, and it is not related to their previous decision. In contrast, people should not be compensated, if they suffer in the outcome of bad option luck since having bad option luck is related to their pervious decision, and people are responsible for their decision makings (whether the outcome is good or not), so the people should not be compensated. Moreover, Dworkin illustrates that brute luck and option luck could be connected by insurance; he claims that buying an insurance to prevent the unexpected bad brute luck is a considered decision, so it would be classified in option luck. It will be a good option luck if people suffer in the outcome of bad brute luck because it makes people better off during the suffering period. Also, Dworkin clarifies that the insurance does not take away the distinction between brute luck and option luck (293). I will explain this claim using the student example; if the student has purchased an insurance for traffic accidents, he still suffers in the bad brute luck if he gets crashed by a car since the scenario would be better if he purchased the insurance and does not need to make the insurance claim. However, he is still better off in terms of he has better option
A GAME T H E O R E T I C LOOK AT L I F E I N S U R A N C E UNDERWRITING* JEAN LEMAIRE Universit6 Libre de Bruxelles Tim decision problem o[ acceptance or rejection of life insurance proposals is formulated as a ~vo-person non cooperattve game between the insurer and the set of the proposers Using the mmtmax criterion or the Bayes criterion, ~t ~s shown how the value and the optunal stxateg~es can be computed, and how an optimal s e t of medina!, mformatmns can be selected and utlhzed 1. FORMULATIONOF THE GAME The purpose of this paper, whose m a t h e m a t i c a l level is elementary, is to d e m o n s t r a t e how g a m e t h e o r y can help the insurers to formulate a n d solve some of their
A GAME T H E O R E T I C LOOK AT L I F E I N S U R A N C E UNDERWRITING* JEAN LEMAIRE Universit6 Libre de Bruxelles Tim decision problem o[ acceptance or rejection of life insurance proposals is formulated as a ~vo-person non cooperattve game between the insurer and the set of the proposers Using the mmtmax criterion or the Bayes criterion, ~t ~s shown how the value and the optunal stxateg~es can be computed, and how an optimal s e t of medina!, mformatmns can be selected and utlhzed 1. FORMULATIONOF THE GAME The purpose of this paper, whose m a t h e m a t i c a l level is elementary, is to d e m o n s t r a t e how g a m e t h e o r y can help the insurers to formulate a n d solve some of their underwriting
Taking after Lewis ' model (1989) life insurance demand is settled by a boost of the dependents ' or beneficiaries’ normal lifetime utility. Security of dependent individuals from a family against financial hardship on account of a wage earner 's unexpected passing is a vital thought process of purchasing life insurance. Subsequently, the higher number of dependents suggests expanding demand for life insurance. Then again, various family individuals may constrain the wage earner 's financial sources, inferring negative impacts of families ' individuals on life insurance consumption.
ReferencesDess, GG, Lumpkin, GT, Eisner, AB 2007, 'Strategic management' , 3rd edn, McGraw-Hill, New York.
Of the numerous decisions consummated during a lifetime, a handful will stand apart in rather dramatic fashion compared to more routine activities emblematic of everyday life. These outliers distinguish themselves with the hallmark of long-term repercussions emanating from miscalculation or misunderstood risk which routinely produces an assortment of financial peril. Such exceedingly prodigious decisions primarily categorize as strategic with their formulation amalgamations of art, science and a smattering of other intangible elements. Undoubtedly, they ought to warrant extraordinary care and thorough investigation going forward, including possible exit strategies. However, time and again, the human equation proves otherwise and omits that
Picture if you will a group of people making decisions. The decisions that are made do not have to be significant at all. They have to be just significant to the situation at hand. This concept is considered to mathematicians as Game Theory. Game Theory is broken down into tree different types of games. As stated by Thomas S. Ferguson of UCLA “There are three main mathematical models or forms used in the study of games, the extensive form, the strategic form and the coalitional form”. Some games that are the most popular to being discussed in Game Theory are chess, checkers, and tic-tac-toe (Ferguson). There are also different terms that are used in this theory as well. Some of the major terms are The Nash Equilibrium,
Names an example or context in which the term is applied, with an illustration available in the appendices.
The data was collected in controlled lab-in-the-field experiments carried out in Ethiopia. Insurance games were conducted with iddir members in addition to general information being collected specifically relating to these individuals .The games were carried out with an attached monetary reward, with the aim of gaining an understanding of the decision-making process of members given a particular scenario. There were four different sessions conducted in which members of the same iddir took part in particular games: the Index insurance with risk-sharing game, the index insurance without risk-sharing game , the indemnity insurance with risk-sharing game and the indemnity insurance without risk-sharing game. In each information environment, those participating in the experiment were given the choice to purchase 0, 1 or 2 units of insurance. Each session consisted of 40 members, with 10 sessions being conducted in total. Thus, 400 farmers were observed in total. There were 240 individuals participating in the indemnity sessions and 160 involved in the index sessions. Full training was given to farmers in the form of interactive games, with information and instructions being read out to those participating in the study before the final games were played. The purpose of this was to ensure that the farmers were capable of making informed decisions with regards to the risks that they were willing to take.