1,721,025 research outputs found
Invariant measures for the Musiela equation with deterministic diffusion term
Full text linkIn this article the forward rates equation of the Musiela model is analysed. The equation is studied in the Sobolev spaces H1(R+) and H1(R+). Explicit mild solutions and equivalent conditions for the existence and uniqueness of invariant measures are presented
Robustness for path-dependent volatility models
Full text linkIn this paper, we consider a generalisation of the Hobson–Rogers model proposed by Foschi and Pascucci (Decis Econ Finance 31(1):1–20, 2008) for financial markets where the evolution of the prices of the assets depends not only on the current value but also on past values. Using differentiability of stochastic processes with respect to the initial condition, we analyse the robustness of such a model with respect to the so-called offset function, which generally depends on the entire past of the risky asset and is thus not fully observable. In doing this, we extend previous results of Blaka Hallulli and Vargiolu (2007) to contingent claims, which are globally Lipschitz with respect to the price of the underlying asset, and we improve the dependence of the necessary observation window on the maturity of the contingent claim, which now becomes of linear type, while in Blaka Hallulli and Vargiolu (2007), it was quadratic. Finally, in this framework, we give a characterisation of the stationarity assumption used in Blaka Hallulli and Vargiolu (2007), and prove that this model is stationary if and only if it is reduced to the original Hobson-Rogers model. We conclude by calibrating the model to the prices of two indexes using two different volatility shapes
Elementi di Probabilita' e Statistica
No full textQuesto libro, rivolto in particolare agli studenti di aree medico-biologiche, presenta le metodologie statistiche piu' usate nella pratica, con una necessaria introduzione ai concetti fondamentali del calcolo delle probabilita'. Ogni capitolo termina con alcuni esercizi risolti, che spesso contengono casi tratti dalla letteratura medica o problemi concreti della vita di tutti i giorni, in modo da interessare gli studenti e da fissare meglio la comprensione delle procedure statistiche. Il teso presuppone la conoscenza del calcolo in una variabile ed e' quindi adatto ad un primo corso universitario di statistica
Portfolio optimization in a defaultable Levy driven market model
No full textIn this paper, we analyse a market where the risky assets follow defaultable exponential additive processes, with coefficients depending on the default state of the assets. In this market we show that when an investor wants to maximize a utility function which is logarithmic on both his/her consumption and terminal wealth, his/her optimal portfolio strategy consists in keeping proportions of wealth in the risky assets which only depend on time and on the default state of the risky assets, but not on their price or on current wealth level; this generalizes analogous results of Pasin and Vargiolu (Econ Notes 39:65–90, 2010) in non-defaultable markets without intermediate consumption. We then present several examples of market where one, two or several assets can default, with the possibility of both direct and information-induced contagion, obtaining explicit optimal investment strategies in several cases. Finally, we study the growth-optimal portfolio in our framework and show an example with necessary and sufficient conditions for it to be a proper martingale or a strict local martingale
Robustness of the Black-Scholes approach in the case of options on several assets
No full textIn this paper we analyse a stochastic volatility model that is an extension of the traditional Black-Scholes one. We price European options on several assets by using a superstrategy approach. We characterize the Markov superstrategies, and show that they are linked to a nonlinear PDE, called the Black-Scholes-Barenblatt (BSB) equation. This equation is the Hamilton-Jacobi-Bellman equation of an optimal control problem, which has a nice financial interpretation. Then we analyse the optimization problem included in the BSB equation and give some sufficient conditions for reduction of the BSB equation to a linear Black-Scholes equation. Some examples are given
Explicit solutions for shortfall risk minimization in multinomial models
No full textIn this paper we show how to deal with shortfall risk minimization in significant multinomial models with one or several risky assets. First we solve the problem when the market is complete, finding both the minimall shortfall risk as well as the optimal strategy. Then we solve the problem in the simplest case of an incomplete market, namely in the case of a single risky asset driven by a trinomial model
Optimal portfolio for HARA utility functions in a pure jump multidimensional incomplete market
No full textIn this paper we analyse a pure jump incomplete market where the
risky assets can jump upwards or downwards. In this market we show that, when an investor wants to maximise a HARA utility function of his/her terminal wealth, his/her optimal strategy consists of keeping constant proportions of wealth in the risky assets, thus extending the classical Merton result to this market. Finally, we compare our results with the classical ones in the diffusion case in terms of scalar dependence of portfolio proportions on the risk-aversion coefficient
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