34 research outputs found
A remark on trace properties of K-cycles
In this paper we discuss trace properties of -summable -cycles
considered by A.Connes in [\rfr(Conn4)]. More precisely we give a proof of a
trace theorem on the algebra \A of a --cycle stated in [\rfr(Conn4)],
namely we show that a natural functional on \A is a trace functional. Then we
discuss whether this functional gives a trace on the whole universal graded
differential algebra \Q(\A). On the one hand we prove that the regularity
conditions on -cycles considered in [\rfr(Conn4)] imply the trace property
on \Q(\A). On the other hand, by constructing an explicit counterexample, we
remark that the sole -cycle assumption is not sufficient for such a property
to hold.Comment: 11 pages, plain Te
CVA and vulnerable options pricing by correlation expansions
We consider the problem of computing the Credit Value Adjustment ({CVA}) of a
European option in presence of the Wrong Way Risk ({WWR}) in a default
intensity setting. Namely we model the asset price evolution as solution to a
linear equation that might depend on different stochastic factors and we
provide an approximate evaluation of the option's price, by exploiting a
correlation expansion approach, introduced in \cite{AS}. We compare the
numerical performance of such a method with that recently proposed by Brigo et
al. (\cite{BR18}, \cite{BRH18}) in the case of a call option driven by a GBM
correlated with the CIR default intensity. We additionally report some
numerical evaluations obtained by other methods.Comment: 21 page
Optimal Scaling of Mala for Nonlinear Regression
We address the problem of simulating efficiently from the posterior
distribution over the parameters of a particular class of nonlinear regression
models using a Langevin-Metropolis sampler. It is shown that as the number N of
parameters increases, the proposal variance must scale as N{-1/3} in order to
converge to a diffusion. This generalizes previous results of Roberts and
Rosenthal [J. R. Stat. Soc. Ser. B Stat. Methodol. 60 (1998) 255-268] for the
i.i.d. case, showing the robustness of their analysis
Discounted and Finitely Repeated Minority Games with Public Signals.
We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payoffs Hausdorff-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.Repeated Games; Imperfect Monitoring; Public Equilibria; Private Equilibria; Discount Factor; Pareto-efficiency;
A folk theorem for minority games.
We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). Between the stages, only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payo can be achieved as a uniform equilibrium payo , and as an almost sure equilibrium payo . In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in a unusual way, the pure actions that were played before start of the punishment.Repeated games; imperfect monitoring; public signals
A folk theorem for minority games.
We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.Repeated games; Imperfect monitoring; Public signals;
A moment matching method for option pricing under stochastic interest rates
In this paper we present a simple, but new, approximation methodology for
pricing a call option in a Black & Scholes market characterized by stochastic
interest rates. The method, based on a straightforward Gaussian moment matching
technique applied to a conditional Black & Scholes formula, is quite general
and it applies to various models, whether affine or not. To check its accuracy
and computational time, we implement it for the CIR interest rate model
correlated with the underlying, using the Monte Carlo simulations as a
benchmark. The method's performance turns out to be quite remarkable, even when
compared with analogous results obtained by the affine approximation technique
presented in Grzelak and Oosterlee (2011) and by the expansion formula
introduced in Kim and Kunimoto (1999), as we show in the last section
Discounted and finitely repeated minority games with public signals
We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a nitely repeated version of the game, and we strengthen our previous
result by showing that the set of equilibrium payos Hausdor-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to innity.
We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a nitely repeated version of the game, and we strengthen our previous
result by showing that the set of equilibrium payos Hausdor-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to innity.
We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.Refereed Working Papers / of international relevanc