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中心领域。该项目通过明确考虑未跨越劳动收入风险和生物识别风险(死亡率、发病率)，做出了重要贡献。虽然这两个风险来源对所有家庭都很重要，但它们要么被忽视，要么至少没有同时进行分析。特别是，现有的文献通常做出不切实际的假设，即劳动收入是可对冲的，因为众所周知，无跨度劳动收入的问题很难解决。然而，众所周知，未跨越收入的存在会对消费投资组合决策产生重大影响。我们的项目缩小了这一差距，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识别风险保险市场，并分析未跨越劳动收入风险对保险需求的影响。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困惑。因此，如果考虑到两个最相关的风险来源(劳动力收入和生物统计)，我们的项目将导致对个人消费组合决策的更深层次的理解。其次，我们考虑了一个具有未跨越生物特征风险的模型，例如，这种风险可能来自巨额共同支付，并计算出如果这些未跨越的生物特征风险是可投保的，个人愿意支付的冷漠价格。这可能会导致相关的政策影响。例如，我们可以解决这样的问题，即具有平均健康状况的代理人愿意容忍哪种规模的共同支付，而不会遭受重大的福利损失。在医疗费用激增的老龄化社会，这个问题非常相关，因为共同支付可以用来遏制医疗部门的成本爆炸。此外，它们还缓解了由于特别是高风险代理人可能寻求保险覆盖这一事实而产生的道德风险问题。第三，我们还通过增加业主自住房地产来丰富我们的模型。这是一个相关的扩展，因为除其他外，房子可以作为抵押品来支付医疗费用。或者，它可以被出售，这样收益就可以用来支付养老院护理等服务。因此，拥有一套房子还可以对冲无法投保的生物识别风险。了解业主自住房地产和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，在存在未跨越的事件风险(例如，健康冲击)的情况下，为消费组合问题提供了显式的近最优解决方案。

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).