Miklos Rasonyi, Lukasz Stettner
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.
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In this paper, we introduce a numeraire-free and original probability based framework for financial markets. We reformulate or characterize fair markets, the optional decomposition theorem, superhedging, attainable claims and complete markets in terms of martingale deflators, present a recent result of Kramkov and Schachermayer (1999, 2001) on portfolio optimization and give a review of utility-based approach to contingent claim pricing in incomplete markets.
The main result of the paper is a version of the fundamental theorem of asset pricing (FTAP) for large financial markets based on an asymptotic concept of no market free lunch for monotone concave preferences. The proof uses methods from the theory of Orlicz spaces. Moreover, various notions of no asymptotic arbitrage are characterized in terms of no asymptotic market free lunch; the difference lies in the set of utilities. In particular, it is shown directly that no asymptotic market free lunch with respect to monotone concave utilities is equivalent to no asymptotic free lunch. In principle,…
We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic programming, we characterize the value function with a backward stochastic differential equation and the optimal portfolio policies. We separately treat the cases of exponential, power and logarithmic utility.
We consider a utility maximization problem in a broad class of markets. Apart from traditional semimartingale markets, our class of markets includes processes with long memory, fractional Brownian motion and related processes, and, in general, Gaussian processes satisfying certain regularity conditions on their covariance functions. Our choice of markets is motivated by the well-known phenomena of the so-called "constant" and "variable depth" memory observed in real world price processes, for which fractional and multifractional models are the most adequate descriptions. We introduce the notio…
In this paper, we consider the classical problem of utility maximization in a financial market allowing jumps. Assuming that the constraint set is a compact set, rather than a convex one, we use a dynamic method from which we derive a specific BSDE. We then aim at showing existence and uniqueness results for the introduced BSDE. This allows us to give an explicit expression of the value function and characterize optimal strategies for our problem.
On general financial markets with concave transactions costs
本文研究了具有凹交易成本的金融市场，给出了无套利的充分条件，并引入渐近套利概念分析此类市场。
We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial markets. As a corollary, we obtain existence of an utility maximizer in the frictionless market model, markets with proportional transaction costs and also more general convex costs, like in the case of market impact.
The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the $α$~-~quantile price is shown. The large Black-Scholes model is carefully examined.
We examine weak anticipations in discrete-time and continuous-time financial markets consisting of one risk-free asset and multiple risky assets, defining a minimal probability measure associated with the anticipation that does not depend on the choice of a utility function. We then define the financial value of weak information in the discrete-time economies and show that these values converge to the financial value of weak information in the continuous-time economy in the case of a complete market.
In this paper, we study the dual problem of the expected utility maximization in incomplete markets with bounded random endowment. We start with the problem formulated in the paper of Cvitanić-Schachermayer-Wang (2001) and prove the following statement: in the Brownian framework, the countably additive part $Q^r$ of the dual optimizer $Q\in (L^\infty)^*$ obtained in that paper can be represented by the terminal value of a supermartingale deflator $Y$ defined in the paper of Kramkov-Schachermayer (1999), which is a local martingale.
In order to find a way of measuring the degree of incompleteness of an incomplete financial market, the rank of the vector price process of the traded assets and the dimension of the associated acceptance set are introduced. We show that they are equal and state a variety of consequences.
The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of the market coefficient processes lead to small changes in the agent's optimal behavior derived from the solution of the related utility-maximization problems. Specifically, we identify the topologies on the parameter process space and the solution space under which utility-maximization is a continuous op…
We consider the problem of decomposing monetary risk in the presence of a fully traded market in {\it some} risks. We show that a mark-to-market approach to pricing leads to such a decomposition if the risk measure is time-consistent in the sense of Delbaen.
We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, we require, in addition to the $V$-compactness hypothesis of Larsen and Žitković (2007) (ArXiv: 0706.0474), a local $bmo$ hypothesis, a condition which is seen to always be trivially satisfied in the setting of Larsen and Žitković (2007). For markets of the form $S = M + \int λd<M>$, these conditions are simultaneously implied by the existen…
Utility maximization in constrained and unbounded financial markets: Applications to indifference valuation, regime switching, consumption and Epstein-Zin recursive utility
本专著研究受约束且无界金融市场中的投资者效用最大化问题，结合二次倒向随机微分方程与凸对偶方法，并应用于无差别定价、体制转换及Epstein-Zin递归效用下的投资消费问题。
We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. Simple sufficient conditions are given for the problem to be well-posed, in the sense the optimal wealth and the marginal utility-based prices are continuous functionals of preferences and probabilistic views.
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal constraints.We deal with random endowment density streams which admit jumps and general time-dependent utility functions on which only regularity conditions are imposed. As an integral part of the proof of the main result, we establish a novel characterization of semimartingale functions.
This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage properties of a large market are completely determined by the asymptotic behavior of the sequence of the numéraire portfolios, related to the small markets. The obtained criteria can be expressed in terms of contiguity, entire separation and Hellinger integrals, provided these notions are extended to sub-probability measures. As examples we consider market models o…
We consider idealized financial markets in which price paths of the traded securities are cadlag functions, imposing mild restrictions on the allowed size of jumps. We prove the existence of quadratic variation for typical price paths, where the qualification "typical" means that there is a trading strategy that risks only one monetary unit and brings infinite capital if quadratic variation does not exist. This result allows one to apply numerous known results in pathwise Ito calculus to typical price paths; we give a brief overview of such results.
Metastable Financial Markets
该研究将金融市场视为亚稳态系统，提出相关理论证明金融时间序列以隐马尔可夫模型演化，指出投资波动由市场状态驱动，完善了非平稳时间序列的风险评估方法。
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