We develop a unifying approach for approximating a \limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or \almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...

The success of the big bang predictions for the abundances of the light elements suggests that the universe was already in thermal equilibrium at one second after the big bang. At this time, the region that later evolves to become the observed universe was, in the context of the conventional (non-inflationary) cosmological model, many horizon distances across. Try to estimate how many. You may ...

We consider the classification of static near-horizon geometries of stationary extremal (not necessarily BPS) black hole solutions of five dimensional Einstein-Maxwell theory coupled to a Chern-Simons term with coupling ξ (with ξ = 1 corresponding to supergravity). Assuming the black holes have two rotational symmetries, we show that their near-horizon geometries are either the direct product A...

Are conventional and sustainable cryptocurrencies effective hedging instruments for high cryptocurrency uncertainty? This paper examines co-movements between (Bitcoin, Ethereum, Binance Coin, Tether) (Cardano, Powerledger, Stellar, Ripple) two uncertainty indices (UCRY price UCRY policy). Using weekly returns from 1 October 2017 to 30 March 2021, the employs bivariate wavelet coherence method c...

We study P − V criticality of black holes in Lovelock gravities in the context of horizon thermodynamics. The corresponding first law of horizon thermodynamics emerges as one of the Einstein–Lovelock equations and assumes the universal (independent of matter content) form δE = TδS − PδV , where P is identified with the total pressure of all matter in the spacetime (including a cosmological cons...

A widespread myth asserts that all small universe models suppress the CMB quadrupole. In actual fact, some models suppress the quadrupole while others elevate it, according to whether their low-order modes are weak or strong relative to their high-order modes. Elementary geometrical reasoning shows that a model’s largest dimension determines the rough value lmin at which the CMB power spectrum ...

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of nite horizon MDPs to the innnite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with innnite state space,...

Miller and Modigliani (1961) consider valuation of innnite horizon rms that may not engage in purchasing their own shares. While their fundamental valuation approach applies also to rms that purchase their own shares, their stream of dividends approach does not. The latter approach is modiied so that it can be used for valuation of innnite horizon rms including those which may purchase their ow...

We rephrase the derivation of black hole radiation so as to take into account, at the level of transition amplitudes, the change of the geometry induced by the emission process. This enlarged description reveals that the dynamical variables which govern the emission are the horizon area and its conjugate time variable. Their conjugation is established through the boundary term at the horizon wh...

Exploring long-term implications of valuation leads us to recover and use a distorted probability measure that reflects the long-term implications for risk pricing. Formally, we apply a generalized version of Perron-Frobenius theory to construct this probability measure. We discuss methods for recovering this distribution from financial market data; we apply this distribution to characterize th...