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Stochastic Growth: A Duality Approach (JET, Vol. 113 (2003), p131-143.)
Abstract We re-examine the representative agent's optimal consumption and savings under uncertainty in the presence of investment constraints using martingale representation and convex analysis techniques. This framework allows quantifying explicitly precautionary savings motive that induces a higher average growth rate than in a certainty set up. We provide a closed form solution for a Cobb-Douglas economy. The effect of uncertainty on portfolio selection is analyzed. Consumption growth rate and risk free interest rate exhibit a U shape relationship. Uncertainty negatively affects expected consumption growth rate; such a result seems to be supported by empirical evidence.
JEL classification: C61, D90, O41.
Keywords: Stochastic Growth, Convex Analysis, Precautionary Savings.

Asset Prices in an Exchange Economy when Agents Have Heterogeneous Homothetic Recursive Preferences and No Risk Free Bond is Available  (JEDC, Vol. 35 (2011), p80-96.)
Abstract We study a pure exchange economy under incomplete markets where households have heterogeneous homothetic recursive preferences and lending and borrowing are precluded. We fully characterize the properties of the efficient allocations and the equilibrium asset price. The ownership distribution dynamics reveal the emergence of a dominant agent, who after some finite time, remains the only investor that increases asset holdings until asymptotically owning the entire wealth. Investors can be ranked according to a unique parameter that aggregates agents' preference characteristics and we show how time discount rate, attitude towards risk and intertemporal substitution contribute to capital accumulation.
JEL classification: C68, D81, G12.
Keywords: Recursive Preferences, Heterogeneous Agents, General Equilibrium, Ownership Distribution.

Why Does Junior Put All His Eggs in One Basket? A Potential Rational Explanation for Holding Concentrated Portfolios, join with Stathis Tompaidis(UT Austin) and Chunyu  Yang (BI Norwegian Business School) (JFE, Vol. 109 (2013), p775-796)
Abstract Empirical studies of household portfolios show that young households, with little financial wealth, hold under-diversified portfolios that are concentrated in a small number of assets, a fact often attributed to behavioral biases. We present a potential rational alternative: we show that investors with little financial wealth, who receive labor income, rationally limit the number of assets they invest in when faced with financial constraints such as margin requirements and   restrictions on borrowing. We provide a theoretical and numerical support for our results and identify the ratio of wealth to labor income as useful control variable for household portfolio studies.
JEL classification: D81, D83, E21, G11.
Keywords: Asset Selection, Under-diversification, Labor Income, Financial Constraints, Household Portfolios.

Manuscripts under Review

Optimal Consumption and Investment Strategies under Wealth Ratcheting (Invited to revise and resubmit to JET)
Abstract Individuals driven by capital accumulation may be reluctant to experience large wealth downfalls. Implications for optimal consumption and investment policies are explored in a dynamic setting where wealth is restrained from falling below a fraction of its all-time high. Risky investment regulates wealth growth and mitigates the ratchet effect of the constraint, and may decrease as wealth approaches its maximum. The correspondence found between habit formation over consumption and wealth ratcheting provides a rational explanation for the extensive use of such a practice in investment management. An extension embeds the spirit of capitalism using wealth as an index for social status.
JEL Classification: D81, E21, G11.
Keywords: Optimum Portfolio Rules, Ratchet Effect, Endogenous Habit Formation.

Intertemporal Allocations under Undiversifiable Labor Income: A Duality Approach (submitted to JEDC)
Abstract We revisit the optimal consumption-investment problem for an infinitely lived isoelastic utility agent who is unable to borrow against her non-insurable future labor income. Using duality techniques, we show that an income growth mean preserving spread lowers consumption and risk tolerance compared to the perfect market framework; equity holdings are dampened (enhanced) whenever income increases (decreases) stock demand under complete markets. Moreover, consumption is further reduced compared to the insurable income setting. Fixing total income volatility, numerical simulations implemented using a shooting method reveal a drastic drop in consumption for small wealth to income ratios as undiversifiable income risk limits hedging and the value of human capital is at its lowest.
JEL classification: D81, E21, G11.
Keywords:  Optimum Portfolio Rules, Incomplete Markets, Labor Income, Background Risk, Duality Techniques, Shooting Method.

Working Papers

Rent-to-Own Usurers? Theory and Empirical Evidence, join with Sanjiv Jaggia (Cal Poly)
Abstract We develop a theoretical framework, assuming a zero-profit industry, to explore the pricing mechanism of a rent to own agreement. It accounts for the agreement's unique features such as the return or early purchase options and free delivery and service. Using detailed transactional data, we infer how customers exercise these options to calibrate our model for several product categories, contractual lengths and payment periodicity. For reasonable parameter values, the model is able to generate very large APRs, most notably for short term contracts with weekly payment schedules. However, these values are significantly lower than the observed rates.
JEL Classification: C24, D14, G29.
Keywords:  Cross Subsidization; Embedded Options; Financially Constrained; Rent-to-Own; Subprime Lending.

Debt Financing Irreversible Investment
Abstract   This paper endogenizes the cost of external funds and explores their impact on undertaking an irreversible investment. The investment strategy incorporates equilibrium feedback that result from a bargaining process between equityholders and a lender; contrary to debt issuance, tax benefits and distress costs cannot be internalized by the firm. "Bad news" are less costly for the firm that has incentives to accelerate investment whereas creditors intend to delay it; under-investment or over-investment is determined by each party relative bargaining power and the size of bankruptcy costs. Default and credit market imperfections raise the effective cost of capital, which dampens the value of waiting. The impact of assets already in place, bankruptcy costs and leverage level are also examined.
JEL classification: C78, D92, E22, G32, G33.
Keywords: Option Value, Irreversible Investment, Debt, Sequential Bargaining, Nash Bargaining.
Speculative Bubbles in a Pure Exchange Economy
Abstract We develop a complete market equilibrium model where two identical isoelastic individuals have heterogeneous expectations. We identify three ingredients for a bubble to form: (i) low risk aversion; (ii) belief dispersion and; (iii) fairly even wealth distribution. Belief disagreements lead agents to take opposite leveraged positions: high stock prices prevail when interest rates are low. The speculative premium incorporates differences of opinion in all future contingencies; for risk neutral investors it can be decomposed into a stream of European call options. Allowing for heterogeneity in preferences reveals that only one investor needs to display a low risk aversion to generate a bubble. The case of infinitely risk averse investors is also examined.
JEL Classification: D51, D84, G12.
Keywords: General Equilibrium Theory, Asset Pricing, Heterogeneous Beliefs, Leverage, Speculation.