1,720,990 research outputs found
Replication and shortfall risk in a binomial model with transaction costs
No full textThe shortfall risk is defined as the optimal mean value of the terminal deficit produced by a self-financing portfolio whose initial value is smaller than what is required to replicate a
contingent claim. In this paper we look for an explicit expression for it, as well as for the optimal strategy, when the market model is a binomial model with proportional transaction costs. We first
study replication of European claims which satisfy suitable assumptions. We then investigate the shortfall minimization problem in a framework very similar to that without transaction costs
Almost sure optimality and optimality in probability for stochastic linear-quadratic regulator with partial information
No full textThe minimal k-entropy martingale measure
No full textWe introduce the notion of κ-entropy (κ ∈ R, |κ| ≤ 1), starting from Kaniadakis' (2001, 2002, 2005) one-parameter deformation of the ordinary exponential function. The κ- entropy is in duality with a new class of utility functions which are close to the exponential utility functions, for small values of wealth, and to the power law utility functions, for large values of wealth. We give conditions on the existence and on the equivalence to the basic measure of the minimal κ-entropy martingale measure. Moreover, we provide characterizations of its density as a κ-exponential function. We show that the minimal κ-entropy martingale measure is closely related to both the standard entropy martingale measure and the well known q-optimal martingale measures. We finally establish the convergence of the minimal κ-entropy martingale measure to the minimal entropy martingale measure as κ tends to
Deformed Exponentials and Applications to Finance
Full text linkWe illustrate some financial applications of the Tsallis and Kaniadakis deformed exponential. The minimization of the corresponding deformed divergence is discussed as a criterion to select a pricing measure in the valuation problems of incomplete markets. Moreover, heavy-tailed models for price processes are proposed, which generalized the well-known Black and Scholes mode
Sub-exponentiality in Statistical Exponential Models
Full text linkImprovements in the study of nonparametric maximal exponential models built on
Orlicz spaces are proposed. By exploiting the notion of sub-exponential random variable, we give theoretical results which provide a clearer insight into the structure of
thesemodels. The explicit constantswe obtainwhen changing the lawof Orlicz spaces
centered at connected densities allow us to derive uniform bounds with respect to a
reference density
On mean-variance optimal reinsurance-investment strategies in dynamic contagion claims models
Full text linkWe consider the reinsurance-investment problem under the mean variance criterion in a dynamic contagion model that takes into account self and externally excited claim clustering effects. We find explicit time-consistent reinsurance-investment strategies for a generalized proportional contract in which only losses above a certain level are reinsured. This greater flexibility in the contract mitigates the possible drawback of the primary insurer ceding too much at the expense of profitability, while still ensuring that the higher risks are shared with the reinsurance counterparty
Un approccio Bayesiano alla gestione del rischio in un modello binomiale.
No full textIn questo lavoro si considera, per un modello a tempo discreto, il problema di minimizzazione dello scoperto medio di portafoglio qualora un agente finanziario, accettando qualche rischio, scelga di investire un capitale iniziale inferiore a quello di copertura. Si analizza la duplice situazione in cui la legge che governa la dinamica del titolo rischioso sottostante e' completamente oppure parzialmente nota. In quest'ultimo caso, si adotta l'appoccio adattativo bayesiano descritto in [25]. Nel caso particolare di un modello binomiale, seguendo [24] si derivano formule esplicite sia per lo scoperto ottimale di portafoglio sia per la corrispondente strategia ottimale. Le soluzioni trovate risultano essere una intuitiva estensione di quelle per il classico modello di Cox-Ross-Rubinstein. Vengono poi presentate ulteriori direzioni di ricerca
Forward backward semimartingale systems for utility maximization
No full textWe consider the problem of maximizing the expected utility of terminal wealth with a terminal random liability when the underlying asset price process is a continuous semimartingale. The optimal strategy is characterized in terms of a semimartingale forward backward system of equations. The results cover the cases of exponential, logarithmic and power utilities, which we analyze as illustrative example
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