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Paolo Guasoni

Publications and source records attributed to Paolo Guasoni.

14 recordsLinked to original sources
arXiv2024

Existence of an equilibrium with limited stock market participation and power utilities

For constants $γ\in (0,1)$ and $A\in (1,\infty)$, we prove existence and uniqueness of a solution to the singular and path-dependent Riccati-type ODE \begin{align*} \begin{cases} h'(y) = \frac{1+γ}{y}\big( γ- h(y)\big)+h(y)\frac{γ+ \big((A-γ)e^{\int_y^1 \frac{1-h(q)}{1-q}dq}-A\big)h(y)}{1-y},\quad y\in(0,1), h(0) = γ, \quad h(1) = 1. \end{cases} \end{align*} As an application, we use the ODE solution to prove existence of a Radner equilibrium with homogenous power-utility investors in the limited participation model from Basak and Cuoco (1998).

q-fin.MF↗
arXiv2022

Minimizing the Repayment Cost of Federal Student Loans

Federal student loans are fixed-rate debt contracts with three main special features: (i) borrowers can use income-driven schemes to make payments proportional to their income above subsistence, (ii) after several years of good standing, the remaining balance is forgiven but taxed as ordinary income, and (iii) accrued interest is simple, i.e., not capitalized. For a very small loan, the cost-minimizing repayment strategy dictates maximum payments until full repayment, forgoing both income-driven schemes and forgiveness. For a very large loan, the minimal payments allowed by income-driven schemes are optimal. For intermediate balances, the optimal repayment strategy may entail an initial period of minimum payments to exploit the non-capitalization of accrued interest, but when the principal is being reimbursed maximal payments always precede minimum payments. Income-driven schemes and simple accrued interest mostly benefit borrowers with very large balances.

q-fin.MF↗
arXiv2020

Minimal L^p-Densities with Prescribed Marginals

We derive sharp lower bounds for L^p-functions on the n-dimensional unit hypercube in terms of their p-th marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.

math.PR↗
arXiv2019

Consumption, Investment, and Healthcare with Aging

This paper solves the problem of optimal dynamic consumption, investment, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect Gompertz' law and investment opportunities are constant. Healthcare slows the natural growth of mortality, indirectly increasing utility from consumption through longer lifetimes. Optimal consumption and healthcare imply an endogenous mortality law that is asymptotically exponential in the old-age limit, with lower growth rate than natural mortality. Healthcare spending steadily increases with age, both in absolute terms and relative to total spending. The optimal stochastic control problem reduces to a nonlinear ordinary differential equation with a unique solution, which has an explicit expression in the old-age limit. The main results are obtained through a novel version of Perron's method.

q-fin.MF↗
arXiv2017

The Limits of Leverage

When trading incurs proportional costs, leverage can scale an asset's return only up to a maximum multiple, which is sensitive to its volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long term returns given average volatility. As leverage increases, rising rebalancing costs imply declining Sharpe ratios. Beyond a critical level, even returns decline. Holding the Sharpe ratio constant, higher asset volatility leads to superior returns through lower costs.

q-fin.PM↗
arXiv2015

Hedging, arbitrage and optimality with superlinear frictions

In a continuous-time model with multiple assets described by càdlàg processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality between feasible trading strategies and shadow execution prices with a martingale measure. Utility maximizing strategies exist even if arbitrage is present, because it is not scalable at will.

q-fin.PR↗
arXiv2014

Hedge and Mutual Funds' Fees and the Separation of Private Investments

A fund manager invests both the fund's assets and own private wealth in separate but potentially correlated risky assets, aiming to maximize expected utility from private wealth in the long run. If relative risk aversion and investment opportunities are constant, we find that the fund's portfolio depends only on the fund's investment opportunities, and the private portfolio only on private opportunities. This conclusion is valid both for a hedge fund manager, who is paid performance fees with a high-water mark provision, and for a mutual fund manager, who is paid management fees proportional to the fund's assets. The manager invests earned fees in the safe asset, allocating remaining private wealth in a constant-proportion portfolio, while the fund is managed as another constant-proportion portfolio. The optimal welfare is the maximum between the optimal welfare of each investment opportunity, with no diversification gain. In particular, the manager does not use private investments to hedge future income from fees.

q-fin.PM↗
arXiv2014

Robust Portfolios and Weak Incentives in Long-Run Investments

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage-free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex.

q-fin.PM↗
arXiv2013

Transaction Costs, Trading Volume, and the Liquidity Premium

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly.

q-fin.PM↗
arXiv2012

Long Horizons, High Risk Aversion, and Endogeneous Spreads

For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as the limits of their isoelastic counterparts for high levels of risk aversion. The results are robust with respect to finite horizons, and extend to multiple uncorrelated risky assets. In this setting, we study a Stackelberg equilibrium, led by a risk-neutral, monopolistic market maker who sets the spread as to maximize profits. The resulting endogenous spread depends on investment opportunities only, and is of the order of a few percentage points for realistic parameter values.

q-fin.PM↗
arXiv2012

Portfolios and risk premia for the long run

This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete. Investment opportunities are driven by, and partially correlated with, state variables which follow an autonomous diffusion. The framework nests models of stochastic interest rates, return predictability, stochastic volatility and correlation risk. In models with several assets and a single state variable, long-run portfolios and risk premia admit explicit formulas up the solution of an ordinary differential equation which characterizes the principal eigenvalue of an elliptic operator. Multiple state variables lead to a quasilinear partial differential equation which is solvable for many models of interest. The paper derives the long-run optimal portfolio and the long-run optimal pricing measures depending on relative risk aversion, as well as their finite-horizon performance.

math.PR↗
arXiv2012

Abstract, Classic, and Explicit Turnpikes

Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike states that optimal final payoffs and portfolios converge under their myopic probabilities. In diffusion models with several assets and a single state variable, the classic turnpike demonstrates that optimal portfolios converge under the physical probability; meanwhile the explicit turnpike identifies the limit of finite-horizon optimal portfolios as a long-run myopic portfolio defined in terms of the solution of an ergodic HJB equation.

q-fin.PM↗
arXiv2008

Consistent price systems and face-lifting pricing under transaction costs

In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs. This result applies to a large class of Markovian and non-Markovian models, including geometric fractional Brownian motion. Using the constructed price systems, we show, under very general assumptions, the following ``face-lifting'' result: the asymptotic superreplication price of a European contingent claim $g(S_T)$ equals $\hat{g}(S_0)$, where $\hat{g}$ is the concave envelope of $g$ and $S_t$ is the price of the asset at time $t$. This theorem generalizes similar results obtained for diffusion processes to processes with conditional full support.

q-fin.PR↗