Studying economic behavior under uncertainty it is common to use the theory of insurance demand (Schlesinger (2013)). While there exists a wide range of insurance economics this thesis concentrates on the optimal insurance demand as well as on the interaction of insurance and saving.

The paper ”Aspects of Rational Insurance Purchasing” by Mossin (1968) can be clearly seen as the start of the research regarding the optimal insurance demand. The well-known results of the author determine the optimal insurance demand by including the topics optimal insurance coverage, risk aversion of the decision-maker and her/his financial status. Mossin (1968) argues that the decision-maker insures a risk completely if the insurance is priced in a fair way. An actuarially fair priced insurance implies that the premium required for the insurance is equal to the expected loss. Consequently, the expected profit for the insurer is equal to zero. As soon as the insurer requires a premium higher than the expected loss it is optimal to choose partial coverage only so that the decision-maker bears a part of the possible loss. The degree of risk aversion reveals how much coverage the decision-maker wants to buy and which amount s/he is willing to pay for it. If the decision-maker is highly risk avers s/he tries to insure a large part of the risk (of course, depending on the price for insurance) while less risk aversion leads to less coverage. The impact of risk aversion on the demand for insurance thereby strongly depends on her/his financial status. Thus, decreasing risk aversion in combination with a higher wealth will lead to the case that the decision-maker is willing to pay less for insurance and also chooses less coverage.

Consequently, risk aversion is one of the crucial elements considering the optimal insurance demand. To better understand the behavior of the decision-maker concerning her/his risk aversion we therefore split up the overall risk preferences into time and risk preferences (Chapter 2). The risk preferences cover the risk aversion of the decision-maker described before and thus the aversion against a possible loss within a period. The time preferences are an additional element to specify the overall risk preferences and cover the risk aversion of the decision-maker over several periods. Hence, the aversion against changes in wealth over time.

The joint decision on optimal saving and insurance dates back to Dionne and Eeckhoudt (1984) who show that saving and insurance can be substitutes. We add to the literature on the joint decision using the described risk and time preferences. Thus, we are left with a more detailed analysis regarding the impact of risk aversion. Interestingly, we show that saving and insurance are substitutes depending on the risk preferences of the decision-maker. If this aversion against a possible loss increases the decision-maker prefers to insure instead to save. In contrast, the time preferences (the aversion against changes in wealth over time) only change the saving amount without influencing the insurance decision.

The applied theories are another important aspect within the theory of insurance demand. Over the years the famous results of Mossin (1968) were doubted, e.g. because of the expected utility approach which is sometimes not able to explain the behavior of the decision-maker properly (e.g. Loubergé (2013) and Chapter 3). Especially, the optimal insurance demand regarding low probability high consequence (LPHC) risks versus high probability low consequence (HPLC) risks reveals inconsistent behavior of the decision- maker by looking at theoretical and empirical work. On the one hand empirical studies detect a rather low insurance demand for LPHC-risks characterized by occasional but sever loss, e.g. caused by a flood or a thunderstorm. On the other hand one observes a high insurance demand for HPLC-risks which occur often but result in only small losses, e.g. a mobile phone or bicycle theft.

These observations are not in line with expected utility theory (EUT) which predicts a high demand for catastrophic insurance compared to mobile phone or bicycle insurance and are referred to as ”insurance puzzle”. In this sense, the thesis evaluates the literature regarding the insurance demand for LPHC- versus HPLC-risks to figure out which insurance is preferred (Chapter 3). Thereby, a necessary step is to analyze the most applied theories within literature. Therefore, we explain the theories based on EUT and prospect theory (PT). While EUT is one of the economic theories, PT belongs to the field of behavioral economics and integrates behavioral aspects to explain insurance decisions.

As a further step, we then include other behavioral concepts, e.g. regret theory. We add to the existing literature by evaluating the explanatory power of the theories regarding the optimal insurance demand for LPHC- and HPLC-risks. Despite the weaknesses, EUT is still often used within the literature regarding insurance decisions to specify the optimal insurance demand. For this reason we use the basic insurance model (based on EUT) as a starting point for our analysis (Chapter 4). We complement the literature by showing within a model based approach that the insurance against LPHC-risks is indeed preferred. Afterwards, we explain the so-called ”insurance puzzle”, e.g. by using behavioral aspects. Thus, we are able show within a theoretical approach that both is possible: the optimal insurance demand can be higher for LPHC-risks but also for HPLC-risks.