On the microstructure and properties of complex concentrated bcc solid solution and tetragonal D8m M5Si3 silicide phases in a refractory complex concentrated alloy

In this work, the refractory complex concentrated alloy (RCCA) 3.5Al–4Cr–6Ge–1Hf–5Mo–36Nb–22Si–1.5Sn–20Ti–1W (at.%) was studied in the as cast and heat treated conditions (100 h or 200 h at 1500 °C). There was strong macrosegregation of Si in the 0.6 kg button/ingot of the cast alloy, in which A2 solid solution, D8m βNb5Si3, C14-NbCr2 Laves phase and Tiss and a ternary eutectic of the A2, D8m and C14 phases were formed. The partitioning of Ti in the as cast and heat treated microstructure and its relationships with other solutes was shown to be important for the properties of the A2 solid solution and the D8m βNb5Si3, which were the stable phases at 1500 °C. The near surface microstructure of the alloy was contaminated with oxygen after heat treatment under flowing Ar. For the aforementioned phases, it was shown, for the first time, that there are relationships between solutes, between solutes and the parameters VEC, Δχ and δ, between the said parameters, and between parameters and phase properties. For the contaminated with oxygen solid solution and silicide, trends in relationships between solutes, between solutes and oxygen content and between the aforementioned parameters and oxygen content also were shown for the first time. The nano-hardness and Young’s modulus of the A2 solid solution and the D8m βNb5Si3 of the as cast and heat-treated alloy were measured using nanoindentation. Changes of nano-hardness and Young’s modulus of the A2 solid solution and D8m βNb5Si3 per solute addition for this multiphase RCCA were discussed. The nano-hardness and Young’s modulus of the solid solution and the βNb5Si3, respectively, were 9.5 ± 0.2 GPa and 177.4 ± 5.5 GPa, and 17.55 ± 0.5 GPa and 250.27 ± 6.3 GPa after 200 h at 1500 °C. The aforementioned relationships and properties of the two phases demonstrated the importance of synergy and entanglement of solutes, parameters and phases in the microstructure and properties of the RCCA. Implications of synergy and entanglement for the design of metallic ultra-high temperature materials were emphasised

Arbitrage and utility maximization in market models with an insider

We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an (Formula presented.)-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails. © 2018 Springer-Verlag GmbH Germany, part of Springer Natur

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

Finite-Dimensional Representations for Controlled Diffusions with Delay

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay. © 2014, Springer Science+Business Media New York

Arbitrage Opportunities in Misspecified Stochastic volatility Models

There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strategies which maximize the arbitrage profit. In the case when the misspecified dynamics is a classical Black-Scholes one, we give a new interpretation of the classical butterfly and risk reversal contracts in terms of their (near) optimality for arbitrage strategies. Our results are illustrated by a numerical example including transaction costs.