共查询到10条相似文献,搜索用时 78 毫秒
1.
We present a pathwise approach to continuous-time finance based on causal functional calculus. Our framework does not rely on any probabilistic concept. We introduce a definition of continuous-time self-financing portfolios, which does not rely on any integration concept and show that the value of a self-financing portfolio belongs to a class of nonanticipative functionals, which are pathwise analogs of martingales. We show that if the set of market scenarios is generic in the sense of being stable under certain operations, such self-financing strategies do not give rise to arbitrage. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. Applying the transition principle of Rufus Isaacs in differential games, we obtain a pathwise dynamic programming principle for the superhedging cost. We show that the superhedging cost is characterized as the solution of a path-dependent equation. For the Asian option, we obtain an explicit solution. 相似文献
2.
A Microeconomic Approach to Diffusion Models For Stock Prices 总被引:1,自引:0,他引:1
This paper studies a class of diffusion models for stock prices derived by a microeconomic approach. We consider discrete-time processes resulting from a market equilibrium and then apply an invariance principle to obtain a continuous-time model. the resulting process is an Ornstein-Uhlenbeck process in a random environment, and we analyze its qualitative behavior. In particular, we provide simple criteria for the stability or instability of the corresponding stock price model, and we give explicit formulae for the invariant distributions in the recurrent case. 相似文献
3.
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real‐world instance. 相似文献
4.
We consider a consumption and investment problem where the market presents different regimes. An investor taking decisions continuously in time selects a consumption–investment policy to maximize his expected total discounted utility of consumption. The market coefficients and the investor's utility of consumption are dependent on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. We obtain explicit optimal consumption and investment policies for specific HARA utility functions. We show that the optimal policy depends on the regime. We also make an economic analysis of the solutions, and show that for every investor the optimal proportion to allocate in the risky asset is greater in a "bull market" than in a "bear market." This behavior is not affected by the investor's risk preferences. On the other hand, the optimal consumption to wealth ratio depends not only on the regime, but also on the investor's risk tolerance: high risk-averse investors will consume relatively more in a "bull market" than in a "bear market," and the opposite is true for low risk-averse investors. 相似文献
5.
In a recent paper ( Jin, Yan, and Zhou 2005 ), it is proved that efficient strategies of the continuous-time mean–semivariance portfolio selection model are in general never achieved save for a trivial case. In this note, we show that the mean–semivariance efficient strategies in a single period are always attained irrespective of the market condition or the security return distribution. Further, for the below-target semivariance model the attainability is established under the arbitrage-free condition. Finally, we extend the results to problems with general downside risk measures. 相似文献
6.
Mohamed Belhaj 《Mathematical Finance》2010,20(2):313-325
We consider a model in which a firm faces two types of liquidity risks: a Brownian risk and a Poisson risk. The firm chooses a dividend policy to maximize shareholder value. We characterize the optimal firm value and we show that the optimal dividend policy is a barrier strategy: the firm keeps cash inside when the cash reserves level is less than a critical threshold and pays cash in excess of this threshold. We also analyze the problem of insurance against the Poisson risk. We find that it is optimal for the firm to buy full insurance when its cash reserves are above a critical threshold and not to insure otherwise. 相似文献
7.
We consider the problem of pricing derivative securities which involve a barrier clause. We give general techniques to calculate, or estimate accurately, barrier option prices, using methods for estimating diffusion process boundary hitting times. The solution gives a simple, easy–to–use, method for calculating barrier option prices. 相似文献
8.
In this paper, we provide a model for diffusion of products, which are available in limited quantity until a known expiration date, after which the unsold products have no value. We consider the case of a performing arts company. The model development is built on the foundation of classical product diffusion model by Bass (1969) and the psychological effect known as the scarcity principle (Cialdini, 1985). Our empirical analysis results show that the proposed model can provide significant improvement in prediction of the products characterized by the scarcity effect. 相似文献
9.
Conditions suitable for applications in finance are given for the weak convergence (or convergence in probability) of stochastic integrals. For example, consider a sequence Sn of security price processes converging in distribution to S and a sequence θn of trading strategies converging in distribution to θ. We survey conditions under which the financial gain process θn dSn converges in distribution to θ dS. Examples include convergence from discrete- to continuous-time settings and, in particular, generalizations of the convergence of binomial option replication models to the Black-Scholes model. Counterexamples are also provided. 相似文献
10.
We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the “wealth process” is a supermartingale. Next, we prove the existence of an optimal solution to the portfolio optimization problem of maximizing utility from terminal wealth in the same model, we also characterize this solution via a transformation to a hedging problem: the optimal portfolio is the one that hedges the inverse of marginal utility evaluated at the shadow state-price density solving the corresponding dual problem, if such exists. We can then use the optimal shadow state-price density for pricing contingent claims in this market. the mathematical tools are those of continuous-time martingales, convex analysis, functional analysis, and duality theory. 相似文献