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This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence.
I numerically solve realistically calibrated life cycle consumption-investment problems in continuous time featuring stochastic mortality risk driven by jumps, unspanned labor income as well as short-sale and liquidity constraints and a simple insurance. I compare models with deterministic and stochastic hazard rate of death to a model without mortality risk. Mortality risk has only minor effects on the optimal controls early in the life cycle but it becomes crucial in later years. A diffusive component in the hazard rate of death has no significant impact, whereas a jump component is desired by the agent and influences optimal controls and wealth evolution. The insurance is used to ensure optimal bequest such that there is no accidental bequest. In the absence of the insurance, the biggest part of bequest is accidental.
Consumption-based asset pricing with rare disaster risk : a simulated method of moments approach
(2014)
The rare disaster hypothesis suggests that the extraordinarily high postwar U.S. equity premium resulted because investors ex ante demanded compensation for unlikely but calamitous risks that they happened not to incur. Although convincing in theory, empirical tests of the rare disaster explanation are scarce. We estimate a disaster-including consumption-based asset pricing model (CBM) using a combination of the simulated method of moments and bootstrapping. We consider several methodological alternatives that differ in the moment matches and the way to account for disasters in the simulated consumption growth and return series. Whichever specification is used, the estimated preference parameters are of an economically plausible size, and the estimation precision is much higher than in previous studies that use the canonical CBM. Our results thus provide empirical support for the rare disaster hypothesis, and help reconcile the nexus between real economy and financial markets implied by the consumption-based asset pricing paradigm.
We show theoretically that income redistribution benefits borrowingconstrained individuals more than is implied by standard relative-income and uninsurable-risk considerations. Empirically, we find in international opinion-survey data that younger and lower-income individuals express stronger support for government redistribution in countries where consumer credit is less easily available. This evidence supports our theoretical perspective if such individuals are more strongly affected by tighter credit supply, in that expectations of higher incomes in the future increase their propensity to borrow. JEL Classification: E21
We show that the optimal consumption of an individual over the life cycle can have the hump shape (inverted U-shape) observed empirically if the preferences of the individual exhibit internal habit formation. In the absence of habit formation, an impatient individual would prefer a decreasing consumption path over life. However, because of habit formation, a high initial consumption would lead to high required consumption in the future. To cover the future required consumption, wealth is set aside, but the necessary amount decreases with age which allows consumption to increase in the early part of life. At some age, the impatience outweighs the habit concerns so that consumption starts to decrease. We derive the optimal consumption strategy in closed form, deduce sufficient conditions for the presence of a consumption hump, and characterize the age at which the hump occurs. Numerical examples illustrate our findings. We show that our model calibrates well to U.S. consumption data from the Consumer Expenditure Survey.
he observed hump-shaped life-cycle pattern in individuals' consumption cannot be explained by the classical consumption-savings model. We explicitly solve a model with utility of both consumption and leisure and with educational decisions affecting future wages. We show optimal consumption is hump shaped and determine the peak age. The hump results from consumption and leisure being substitutes and from the implicit price of leisure being decreasing over time; more leisure means less education, which lowers future wages, and the present value of foregone wages decreases with age. Consumption is hump shaped whether the wage is hump shaped or increasing over life.
The complexities of geopolitical events, financial and fiscal crises, and the ebb and flow of personal life circumstances can weigh heavily on individuals’ minds as they make critical economic decisions. To investigate the impact of cognitive load on such decisions, the authors conducted an incentivized online experiment involving a representative sample of 2,000 French households. The results revealed that exposure to a taxing and persistent cognitive load significantly reduced consumption, particularly for individuals under the threat of furlough, while simultaneously increasing their account balances, particularly for those not facing such employment uncertainty. These effects were not driven by supply constraints or a worsening of credit constraints. Instead, cognitive load primarily affected the optimality of the chosen policy rules and impaired the ability of the standard economic model to accurately predict consumption patterns, although this effect was less pronounced among college-educated subjects
Consuming dividends
(2020)
This paper studies why investors buy dividend-paying assets and how they time their consumption accordingly. We combine administrative bank data linking customers’ consumption transactions and income to detailed portfolio data and survey responses on financial behavior. We find that private consumption is excessively sensitive to dividend income. Investors across wealth, income, and age distributions increase spending precisely around days of dividend receipt. Importantly, the consumption response is driven by financially prudent investors who select dividend portfolios, anticipate dividend income, and plan consumption accordingly. Our results contribute to the literature on a dividend clientele and provide evidence of ‘planned’ excess sensitivity.
Search costs for lenders when evaluating potential borrowers are driven by the quality of the underwriting model and by access to data. Both have undergone radical change over the last years, due to the advent of big data and machine learning. For some, this holds the promise of inclusion and better access to finance. Invisible prime applicants perform better under AI than under traditional metrics. Broader data and more refined models help to detect them without triggering prohibitive costs. However, not all applicants profit to the same extent. Historic training data shape algorithms, biases distort results, and data as well as model quality are not always assured. Against this background, an intense debate over algorithmic discrimination has developed. This paper takes a first step towards developing principles of fair lending in the age of AI. It submits that there are fundamental difficulties in fitting algorithmic discrimination into the traditional regime of anti-discrimination laws. Received doctrine with its focus on causation is in many cases ill-equipped to deal with algorithmic decision-making under both, disparate treatment, and disparate impact doctrine. The paper concludes with a suggestion to reorient the discussion and with the attempt to outline contours of fair lending law in the age of AI.
Search costs for lenders when evaluating potential borrowers are driven by the quality of the underwriting model and by access to data. Both have undergone radical change over the last years, due to the advent of big data and machine learning. For some, this holds the promise of inclusion and better access to finance. Invisible prime applicants perform better under AI than under traditional metrics. Broader data and more refined models help to detect them without triggering prohibitive costs. However, not all applicants profit to the same extent. Historic training data shape algorithms, biases distort results, and data as well as model quality are not always assured. Against this background, an intense debate over algorithmic discrimination has developed. This paper takes a first step towards developing principles of fair lending in the age of AI. It submits that there are fundamental difficulties in fitting algorithmic discrimination into the traditional regime of anti-discrimination laws. Received doctrine with its focus on causation is in many cases ill-equipped to deal with algorithmic decision-making under both, disparate treatment, and disparate impact doctrine. The paper concludes with a suggestion to reorient the discussion and with the attempt to outline contours of fair lending law in the age of AI.