This work provides an application of wavelet analysis to pricing and hedging path–dependent contingent claims within the framework of the Black–Scholes model.

The double barrier option is characterized by pay-off with strike K, maturity T, upper Su and lower Sd barrier levels and the corresponding rebates φu and φd which can be time dependent. We divide last four quantities by strike K and introduce new variables x = ln(S/K), xu = ln(Su/K), xd = ln(Sd/K). The value of European double barrier call option U(t, x) satisfies the extended Black-Scholes eq...

We have written S = S(t); B = B(t); V = V (t) and dW = dW (t) for notational convenience. We also assume the portfolios are self-…nancing, which implies that changes in portfolio value are due to changes in the value of the three instruments, and nothing else. Under this setup, any of the instruments can be replicated by forming a replicating portfolio of the other two instruments, using the co...

We consider statistical ensembles of Schwarzschild black holes and prove that these ensembles describe black holes of non vanishing temperatures. The mean space-times associated to these ensembles are explored through exact computations of their energy distributions, total masses and calorific capacities. We discuss our results, with special emphasis on their connections with current and near f...

The multi-parameter character of supersymmetric dark-matter models implies the combination of their experimental studies with astrophysical and cosmological probes. The physics of the early Universe provides nontrivial effects of non-equilibrium particles and primordial cosmological structures. Primordial black holes (PBHs) are a profound signature of such structures that may arise as a cosmolo...

A. Belhaj, M. Chabab,b,1 H. El Moumni, K. Masmar, M.B. Sedra and A. Segui Département de Physique, Faculté Polydisciplinaire, Université Sultan M. Slimane, Béni Mellal, Morocco High Energy Physics and Astrophysics Laboratory, FSSM, Cadi Ayyad University, Marrakesh, Morocco Université Mohammed Premier, Ecole Nationale des Sciences Appliquées, Al Hoceima, Morocco Département de Physique, LHESIR, ...

We consider a popular problem in finance, option pricing, through the lens of an online learning game between Nature and an Investor. In the Black-Scholes option pricing model from 1973, the Investor can continuously hedge the risk of an option by trading the underlying asset, assuming that the asset’s price fluctuates according to Geometric Brownian Motion (GBM). We consider a worst-case model...

Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they are conformally related to the matching of different solutions of constant curvature by means of an improper conformal transformation. The wormholes can be con...

We discuss a previous attempt at a microscopic counting of the entropy of asymptot-ically flat non-extremal black-holes. This method used string dualities to relate 4 and 5 dimensional black holes to the BTZ black hole. We show how the dualities can be justified in a certain limit, equivalent to a near horizon limit, but the resulting spacetime is no longer asymptotically flat.