1,721,025 research outputs found
No Free Lunch under Transaction Costs for Continuous Processes
No full textWe present a version of the Fundamental Theorem of Asset Pricing and of the Hedging Theorem for security markets under transaction costs for continuous processes. We show that the
nflvr condition, which requires that absence of arbitrage is preserved under a smaller bid-ask spread, is equivalent to the existence of a Uniformly Strictly Consistent Price System. We also characterize the superreplication price of bounded contingent claim as the supremum of expected values under all Uniformly Consistent Price Systems
Asymmetric information in fads models
No full textFads models were introduced by Shiller (Am Econ Rev 71:421-436, 1981) and Summers (J Finance 41:591-601, 1986) as plausible alternatives to the efficient markets/constant expected returns assumptions. Under these models, logarithms of asset prices embody both a martingale component, with permanent shocks, and a stationary component, with temporary shocks. We study a continuous-time version of these models both from the point of view of informed agents, who observe both fundamental and market values, and from that of uninformed agents, who only observe market prices. We specify the asset price in the larger filtration of the informed agent, and then derive its decomposition in the smaller filtration of the uninformed agent using the Hitsuda representation of Gaussian processes. For uninformed agents we obtain a non-Markovian dynamics, which justifies the use of technical analysis in optimal trading strategies. For both types of agents, we solve the problem of maximization of expected logarithmic utility from terminal wealth, and obtain an explicit formula for the additional logarithmic utility of informed agents. Finally, we apply the decomposition result to the problem of testing the presence of fads from market data. An application to the NYSE-AMEX indices from the CRSP database shows that, if the fads component prevails, then the mean-reversion speed must be slow
Estimating State Price Densities by Hermite Polynomials: Theory and Application to Italian Derivatives Market
No full textWe study the problem of extracting the state price densities from the market prices of listed options. Adapting a model of Madan and Milne to a multiple expiration setting, we present an estimation method for the risk-neutral probability at a moving horizon of fixed length. With the exception of volatility, all model parameters can be estimated by linear regression and their number can be chosen arbitrarily, depending on the size of the dataset. We discuss empirical issues related to the application of this model to real data and show results on listed options on the Italian MIB30 equity index
Optimal investment with transaction costs and without semimartingales
No full textWe consider a general class of optimization problems in financial markets with incomplete information and transaction costs. Under a no-arbitrage condition strictly weaker than the existence of a martingale measure, and when asset prices are quasi-left-continuous processes, we show the existence of optimal strategies. Applications include maximization of expected utility, minimization of coherent risk measures and hedging of contingent claims
Risk minimization under transaction costs
No full textWe study the general problem of an agent wishing to minimize the risk of a position at a fixed date. The agent trades in a market with a risky asset, with incomplete information, proportional transaction costs, and possibly constraints on strategies. In particular, this framework includes the problems of hedging contingent claims and maximizing utility from wealth. We obtain a minimization problem on a space of predictable processes with finite variation. Borrowing a technique from Calculus of Variation, on this space we look for a convergence which makes minimizing sequences relatively compact, and risk lower semicontinuous. For a class of convex decreasing risk functionals, we show the existence of optimal strategies. Examples include the problems of shortfall minimization, utility maximization, and minimization of coherent risk measures
Consumption in incomplete markets
Full text linkWe develop a method to find approximate solutions, and their accuracy, to consumption–investment problems with isoelastic preferences and infinite horizon, in incomplete markets where state variables follow a multivariate diffusion. We construct upper and lower contractions; these are fictitious complete markets in which state variables are fully hedgeable, but their dynamics is distorted. Such contractions yield pointwise upper and lower bounds for both the value function and the optimal consumption of the original incomplete market, and their optimal policies are explicit in typical models. Approximate consumption–investment policies coincide with the optimal one if the market is complete or utility is logarithmic
Nonlinear price impact and portfolio choice
Full text linkIn a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long-term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square-root impact law and, as extreme cases, linear impact and proportional transaction costs
Rebalancing Multiple Assets with Mutual Price Impact
No full textWe find asymptotically optimal trading policies for long-term investors with constant relative risk aversion, in a multiple-assets market, where expected returns and covariances are constant, and the execution price of each asset is linear in the trading intensities of all assets. Trading toward the frictionless target is optimal, when the current portfolio differs from the target by a principal portfolio—an eigenvector of the inverse impact matrix times the covariance matrix. Optimal policies approach the frictionless target along nonlinear, power-shaped paths, trading faster in more liquid directions, while tolerating wider oscillations along less liquid directions
Shape Optimization Problems over Classes of Convex Domains
No full textWe consider shape optimization problems of the form min I {∫∂A f(x, ν(x)) dHn-1 : A ∈ A} where f is any continuous function and the class A of admissible domains is made of convex sets. We prove the existence of an optimal solution provided the domains satisfy some suitable constraints
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