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1.
Using duality methods, we prove several key properties of the indifference price π for contingent claims. The underlying market model is very general and the mathematical formulation is based on a duality naturally induced by the problem. In particular, the indifference price π turns out to be a convex risk measure on the Orlicz space induced by the utility function. 相似文献
2.
In this paper, we report further progress toward a complete theory of state‐independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions, we establish a surprising Fenchel duality result on conjugate Orlicz spaces, offering a new economic insight into the nature of primal optima and providing a fresh perspective on the classical papers of Kramkov and Schachermayer. The analysis points to an intriguing interplay between no‐arbitrage conditions and standard convex optimization and motivates the study of the fundamental theorem of asset pricing for Orlicz tame strategies. 相似文献
3.
Francesca Biagini Jean‐Pierre Fouque Marco Frittelli Thilo Meyer‐Brandis 《Mathematical Finance》2019,29(1):329-367
We specify a general methodological framework for systemic risk measures via multidimensional acceptance sets and aggregation functions. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario‐dependent allocation). We also provide conditions that ensure monotonicity, convexity, or quasi‐convexity of our systemic risk measures. 相似文献
4.
Francesca Biagini 《Decisions in Economics and Finance》2002,25(1):1-17
The mean-variance hedging approach for pricing and hedging claims in incomplete markets was originally introduced for risky
assets. The aim of this paper is to apply this approach to interest rate models in the presence of stochastic volatility,
seen as a consequence of incomplete information. We fix a finite number of bonds such that the volatility matrix is invertible
and provide an explicit formula for the density of the variance-optimal measure which is independent of the chosen times of
maturity.
Finally, we compute the mean-variance hedging strategy for a caplet and compare it with the optimal stategy according to the
local risk minimizing approach.
Received: 14 July 2000 / Accepted: 10 April 2001 相似文献
5.
This article examines neural network-based approximations for the superhedging price process of a contingent claim in a discrete time market model. First we prove that the α-quantile hedging price converges to the superhedging price at time 0 for α tending to 1, and show that the α-quantile hedging price can be approximated by a neural network-based price. This provides a neural network-based approximation for the superhedging price at time 0 and also the superhedging strategy up to maturity. To obtain the superhedging price process for , by using the Doob decomposition, it is sufficient to determine the process of consumption. We show that it can be approximated by the essential supremum over a set of neural networks. Finally, we present numerical results. 相似文献
6.
We consider an incomplete stochastic financial market where the price processes are described by a vector valued semimartingale
that is possibly non locally bounded. We face the classical problem of utility maximization from terminal wealth, under the
assumption that the utility function is finite-valued and smooth on the entire real line and satisfies reasonable asymptotic
elasticity. In this general setting, it was shown in Biagini and Frittelli (Financ. Stoch. 9, 493–517, 2005) that the optimal
claim admits an integral representation as soon as the minimax σ-martingale measure is equivalent to the reference probability
measure. We show that the optimal wealth process is in fact a supermartingale with respect to every σ-martingale measure with
finite generalized entropy, thus extending the analogous result proved by Schachermayer (Financ. Stoch. 4, 433–457, 2003)
for the locally bounded case.
相似文献
7.
In this article, we deal with optimal dynamic carbon emission regulation of a set of firms. On the one hand, the regulator dynamically allocates emission allowances to each firm. On the other hand, firms face idiosyncratic, as well as common, economic shocks on emissions, and they have linear quadratic abatement costs. Firms can trade allowances so as to minimize total expected costs, which arise from abatement, trading, and terminal penalty. Using variational methods, we first exhibit in closed form the market equilibrium in function of the regulator's dynamic allocation. We then solve the Stackelberg game between the regulator and the firms. The result is a closed-form expression of the optimal dynamic allocation policies that allow a desired expected emission reduction. The optimal policy is unique in the presence of market impact. In absence of market impact, the optimal policy is nonunique, but all the optimal policies share common properties. The optimal policies are fully responsive, and therefore induce a constant abatement effort and a constant price of allowances. Our results are robust to some extensions, like different penalty functions. 相似文献
8.
Sara Biagini Bruno Bouchard Constantinos Kardaras Marcel Nutz 《Mathematical Finance》2017,27(4):963-987
We study a continuous‐time financial market with continuous price processes under model uncertainty, modeled via a family of possible physical measures. A robust notion of no‐arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first main result is a version of the fundamental theorem of asset pricing: holds if and only if every admits a martingale measure that is equivalent up to a certain lifetime. The second main result provides the existence of optimal superhedging strategies for general contingent claims and a representation of the superhedging price in terms of martingale measures. 相似文献
9.
10.
The timing option embedded in a futures contract allows the short position to decide when to deliver the underlying asset during the last month of the contract period. In this paper we derive, within a very general incomplete market framework, an explicit model independent formula for the futures price process in the presence of a timing option. We also provide a characterization of the optimal delivery strategy, and we analyze some concrete examples. 相似文献