Health vs. Wealth: Non-financial life-cycle decisions and their impact on consumption-portfolio choice with unspanned labor income

研究个人的生命周期消费组合问题是金融学研究的一个核心领域。该项目明确考虑了未跨越的劳动收入风险和生物识别风险（死亡率、发病率），这是一个重要的贡献。尽管这两种风险来源对所有家庭都很重要，但它们要么被忽视，要么至少没有同时分析。特别是，现有文献通常做出了一个不切实际的假设，即劳动收入是可以对冲的，因为劳动收入无跨越的问题是出了名的难以解决。然而，众所周知，未跨越收入的存在可以显著影响消费组合决策。我们的项目填补了这一空白，因此可以解决几个相关的研究问题。首先，我们假设存在完整的生物特征风险保险市场，并分析了未跨越的劳动收入风险如何影响保险需求。我们还研究了保险合同的错误定价（例如，由于道德风险或逆向选择问题）是否会挤出保险需求，并可能解释潜在的不参与难题。因此，如果考虑到两个最相关的风险来源（劳动收入和生物特征），我们的项目可以更深入地了解个人的消费组合决策。其次，我们考虑了一个具有无跨越生物特征风险的模型，例如，如果这些无跨越生物特征风险是可保险的，那么我们计算了个人愿意支付的无差异价格。这可能导致相关的政策影响。例如，我们可以解决这样一个问题，即健康状况一般的代理人在不遭受重大福利损失的情况下，愿意承受多大的共同支付额。在一个医疗保健费用激增的老龄化社会，这个问题非常重要，因为共同支付可以用来遏制卫生部门的费用激增。此外，它们减轻了道德风险问题，特别是高风险的代理人可能会寻求保险覆盖。第三，我们还增加了自住房地产，丰富了我们的模式。这是一个相关的扩展，因为除其他事项外，房子可以作为支付医疗费用的抵押品。或者，它可以被出售，这样收益可以用来支付服务，如养老院护理。因此，拥有一所房子也为无法投保的生物特征风险提供了对冲。了解业主自住房地产与健康决策之间的联系是我们要解决的另一个重要问题。最后，我们的项目也做出了重大的理论贡献，因为我们开发了一种数值方法，为存在无跨越事件风险（例如健康冲击）的消费组合问题提供了明确的近最优解决方案。

Studying life-cycle consumption-portfolio problems of individuals is a central field of research in finance. This project makes an important contribution by explicitly taking unspanned labor income risk and biometric risks (mortality, morbidity) into account. Although these two sources of risk are of major importance for all households, they are either disregarded or at least not analyzed simultaneously. In particular, the existing literature usually makes the unrealistic assumption that labor income is hedgeable, since problems with unspanned labor income are notoriously hard to solve. However, it is well known that the presence of unspanned income can significantly influence consumption-portfolio decisions. Our project closes this gap and thus several relevant research questions can be addressed. First, we assume that complete insurance markets for biometric risks exist and analyze how unspanned labor income risk affects insurance demands. We also study whether mispricing of insurance contracts (e.g. due to moral hazard or adverse selection problems) can crowd out insurance demands and might explain potential non-participation puzzles. Therefore, our project leads to a deeper understanding of an individual's consumption-portfolio decision if two of the most relevant risk sources (labor income and biometric) are taken into account. Second, we consider a model with unspanned biometric risks, which for instance might arise from significant copayments, and calculate indifference prices that an individual would be willing to pay if these unspanned biometric risks were insurable. This might lead to relevant policy implications. For instance, we can address the question of which size of copayments an agent with average health status is willing to tolerate without suffering significant welfare losses. In an aging society with exploding health care costs, this issue is very relevant, since copayments can be used to curtail the cost explosion in the health sector. Besides, they mitigate moral hazard issues arising from the fact that especially high-risk agents might seek insurance coverage. Third, we also enrich our model by adding owner-occupied real estate. This is a relevant extension because, among other things, a house can serve as collateral to cover health expenses. Alternatively, it can be sold so that the proceeds can be used to pay for services such as nursing home care. Therefore, owning a house also provides a hedge against uninsurable biometric risks. Understanding the link between owner-occupied real estate and health decisions is another important issue that we address. Finally, our project also makes a significant theoretical contribution since we develop a numerical approach that provides explicit near-optimal solutions to consumption-portfolio problems in the presence of unspanned event risks (e.g. health shocks).