The dynamic programming equation for the problem of optimal investment under capital gains taxes

This paper considers an extension of the Merton optimal investment problem to the case where the risky asset is subject to transaction costs and capital gains taxes. We derive the dynamic programming equation in the sense of constrained viscosity solutions. We next introduce a family of functions, which converges to our value function uniformly on compact subsets, and which is characterized as the unique constrained viscosity solution of an approximation of our dynamic programming equation. In particular, this result justifies the numerical results reported in the accompanying paper by the authors

Modeling continuous-time financial markets with capital gains taxes

We formulate a model of continuous-time financial market consisting of a bank account with constant interest rate and one risky asset subject to capital gains taxes. We consider the problem of maximizing expected utility from future consumption in infinite horizon. This is the continuous-time version of the model introduced by Dammon, Spatt and Zhang [11]. The taxation rule is linear so that it allows for tax credits when capital gains losses are experienced. In this context, wash sales are optimal. Our main contribution is to derive lower and upper bounds on the value function in terms of the corresponding value in a tax-free and frictionless model. While the upper bound corresponds to the value function in a tax-free model, the lower bound is a consequence of wash sales. As an important implication of these bounds, we derive an explicit first order expansion of our value function for small interest rate and tax rate coefficients. In order to examine the accuracy of this approximation, we provide a characterization of the value function in terms of the associated dynamic programming equation, and we suggest a numerical approximation scheme based on finite differences and the Howard algorithm. The numerical results show that the first order Taylor expansion is reasonably accurate for reasonable market data

The welfare effects of tax simplification: a general-equilibrium analysis

An analysis of various schemes for simplifying the U.S. tax system, which finds that a uniform tax system performs almost as well as a system with separate taxes on labor and capital incomes, provided that a depreciation allowance is maintained.Taxation

Trading and the Tax Shelter Value of Depreciable Real Estate

For well-diversified investors in depreciable real estate, the trading decision may be made with the sole objective of maximizing the property's depreciation tax shelter net of all capital gain taxes and transaction costs.This paper develops a dynamic programming model in which the optimal trading strategies and depreciation methods of all investors in a property are simultaneously determined. The effects of inflation, depreciation, recapture and choice of depreciation method are analyzed, and the costs of suboptimal trading are measured. The model is applied to both conventional residential and commercial income properties under post-ERTA tax rules. At single digitinflation rates, properties are traded multiple times, and the costs of suboptimal trading are significant.

Dynamic optimal fiscal and monetary policy in a business cycle model with income redistribution

An estimation of an optimal program of distortionary taxes, money growth, and borrowing to finance a stream of expenditures based on a real business cycle model in which distribution issues between the rich and poor play a fundamental role in policy decisions.Business cycles ; Monetary policy ; Income distribution

EVALUATING FARMLAND INVESTMENTS CONSIDERING DYNAMIC STOCHASTIC RETURNS AND FARMLAND PRICES

This paper examines farmland investment decisions using a stochastic dynamic programming framework. Consideration is given to the dynamic, stochastic nature of farmland returns, linkages between farmland returns and farmland prices, and the effects of the above dynamic factors on a farmÂ’s financial structure. Optimal decisions to purchase or sell farmland are found for a central Illinois farm with high quality farmland. Sizes and debt distributions are then determined, given that the optimal decision rule is followed. Decisions from the dynamic programming model also are compared to a capital budgeting model.Land Economics/Use,

Welfare Gains from Optimal Policy in a Partially Dollarized Economy

This paper evaluates welfare under optimal monetary and fiscal policy in a dynamic stochastic model of currency substitution and capital. It shows that in a partially dollarized economy, the main optimal policy results, i.e. the Friedman Rule and the zero capital tax, hold. Welfare implications of these optimal policies are computed for the Bolivian economy using a second-order approximation technique. The primary conclusions are that the welfare gains under optimal monetary policy are negligible. The welfare gains when optimal fiscal policy is considered alone or in conjunction with optimal monetary policy are sizable and come from the increase in real variables and also by the increase in real balances in local currency. Thus, welfare gains are negatively related to dollarization.Dollarization, Optimal Fiscal and Monetary Policy, Second-order approximation technique.