9,483 research outputs found
Continuous-Time Finite-Horizon Optimal Investment and Consumption Problems with Proportional Transaction Costs
Ph.DDOCTOR OF PHILOSOPH
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.Comment: 29 pages, 5 figures, to appear in "Finance and Stochastics". arXiv
admin note: text overlap with arXiv:1207.733
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. The 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
Portfolio Choice with Stochastic Investment Opportunities: a User's Guide
This survey reviews portfolio choice in settings where investment
opportunities are stochastic due to, e.g., stochastic volatility or return
predictability. It is explained how to heuristically compute candidate optimal
portfolios using tools from stochastic control, and how to rigorously verify
their optimality by means of convex duality. Special emphasis is placed on
long-horizon asymptotics, that lead to particularly tractable results.Comment: 31 pages, 4 figure
Optimal Investment with Transaction Costs and Stochastic Volatility
Two major financial market complexities are transaction costs and uncertain
volatility, and we analyze their joint impact on the problem of portfolio
optimization. When volatility is constant, the transaction costs optimal
investment problem has a long history, especially in the use of asymptotic
approximations when the cost is small. Under stochastic volatility, but with no
transaction costs, the Merton problem under general utility functions can also
be analyzed with asymptotic methods. Here, we look at the long-run growth rate
problem when both complexities are present, using separation of time scales
approximations. This leads to perturbation analysis of an eigenvalue problem.
We find the first term in the asymptotic expansion in the time scale parameter,
of the optimal long-term growth rate, and of the optimal strategy, for fixed
small transaction costs.Comment: 27 pages, 4 figure
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Finite Horizon Portfolio Selection
We study the problem of maximising expected utility of terminal wealth
over a nite horizon, with one risky and one riskless asset available, and
with trades in the risky asset subject to proportional transaction costs.
In a discrete time setting, using a utility function with hyperbolic risk
aversion, we prove that the optimal trading strategy is characterised by
a function of time (t), which represents the ratio of wealth held in the
risky asset to that held in the riskless asset. There is a time varying no
transaction region with boundaries b(t) < s(t), such that the portfo-
lio is only rebalanced when (t) is outside this region. The results are
consistent with similar studies of the in nite horizon problem with in-
termediate consumption, where the no transaction region has a similar,
but time independent, characterisation. We solve the problem numerically
and compute the boundaries of the no transaction region for typical model
parameters. We show how the results can be used to implement option
pricing models with transaction costs based on utility maximisation over
a nite horizo
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
Option Pricing and Hedging with Small Transaction Costs
An investor with constant absolute risk aversion trades a risky asset with
general It\^o-dynamics, in the presence of small proportional transaction
costs. In this setting, we formally derive a leading-order optimal trading
policy and the associated welfare, expressed in terms of the local dynamics of
the frictionless optimizer. By applying these results in the presence of a
random endowment, we obtain asymptotic formulas for utility indifference prices
and hedging strategies in the presence of small transaction costs.Comment: 20 pages, to appear in "Mathematical Finance
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