Portfolio optimization in the case of an asset with a given liquidation time distribution

Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, the seller, on the other hand, can not liquidate his portfolio instantly and waits for a more favorable offer. To minimize losses in this case we need to develop new methods. One of the steps moving the theory towards practical needs is to take into account the time lag of the liquidation of an illiquid asset. This task became especially significant for the practitioners in the time of the global financial crises. Working in the Merton's optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. While a standard Black-Scholes market describes the liquid part of the investment the illiquid asset is sold at a random moment with prescribed liquidation time distribution. In the moment of liquidation it generates additional liquid wealth dependent on illiquid assets paper value. The investor has the logarithmic utility function as a limit case of a HARA-type utility. Different distributions of the liquidation time of the illiquid asset are under consideration - a classical exponential distribution and Weibull distribution that is more practically relevant. Under certain conditions we show the existence of the viscosity solution in both cases. Applying numerical methods we compare classical Merton's strategies and the optimal consumption-allocation strategies for portfolios with different liquidation-time distributions of an illiquid asset.Comment: 30 pages, 1 figur

New materials and technologies for automobile industry

В статье освещена история и современность уральского авто-мобилестроения. В фокусе внимания авторов - производство легковых и грузовых автомобилей, а также материалов и комплектующих к ним. Дана оценка практики и перспектив применения высокопрочных сталей в современном автопроме.This article deals with the history and present of the Ural automotive industry. The authors focus on the production of cars and trucks, as well as materials and components. Given the evaluation of the practices and perspectives of use of high-strength steels in the modern automobile industry

Thermodynamics of reaction of praseodymium with gallium-indium eutectic alloy

Thermodynamic properties of Ga-In eutectic alloys saturated with praseodymium were determined for the first time employing the electromotive force method. The equilibrium potentials of the Pr-In alloys saturated with praseodymium (8.7-12.1 mol.% Pr) and Pr-Ga-In alloys (containing 0.0012-6.71 mol.% Pr) were measured between 573-1073 K. Pr-In alloy containing solid PrIn3 with known thermodynamic properties was used as the reference electrode when measuring the potentials of ternary Pr-In-Ga alloys. Activity, partial and excessive thermodynamic functions of praseodymium in alloys with indium and Ga-In eutectic were calculated. Activity (a), activity coefficients (γ) and solubility (X) of praseodymium in the studied temperature range can be expressed by the following equations: lgaα-Pr(In) = 4.425 - 11965/T ± 0.026. lgα-Pr(Ga-In) = 5.866 - 14766/T ± 0.190. lgγα-Pr(Ga-In) = 2.351 - 9996/T ± 0.39. lgPr(Ga-In) = 3.515 - 4770/T ± 0.20. © 2013 Elsevier B.V. All rights reserved

Study of uranium solubility in gallium-indium eutectic alloy by emf method

Activity, activity coefficients and solubility of uranium in Ga-In eutectic alloy as well as activity of uranium in U-Ga and U-In alloys were determined between 573 and 1073 K using electromotive force (emf) method. © 2013 Pleiades Publishing, Ltd

Thermodynamic properties of lanthanum in gallium-indium eutectic based alloys

Activity and activity coefficients of lanthanum were determined for the first time in gallium-indium eutectic based alloys in a wide temperature range employing electromotive force method. Activity of β-La and super cooled liquid lanthanum in Ga-In eutectic based alloys between 573 and 1073 K linearly depends on the reciprocal temperature: lgaβ-La(Ga-In)=5.660-15, 352T±0.093 lgaLa(Ga-In)=6.074-15,839T±0.093 Activity coefficients of β-La and super cooled liquid lanthanum in this system at 617-1073 K are described by the following equations: lgγβ-La (Ga-In)=3.786-12,216T±0.171 lgγLa(Ga-In)=4. 199-12,703T±0.171 In addition activity of lanthanum in alloys with In was also determined in the same temperature range. © 2012 Elsevier B.V. All rights reserved

Excessive thermodynamic properties of praseodymium in a gallium-indium alloy

The equilibrium potentials of praseodymium-diluted homogeneous Pr-Ga-In alloys in a (Li-K-Cs)Cleut-based salt electrolyte were measured between 573-1073 K by the emf method. These potentials are used to calculate the activity coefficients of α-praseodymium in liquid Ga-In eutectic alloys. PrIn3 alloy with well-known thermodynamic characteristics and without phase transitions in the temperature range 428-1483 K was employed as the reference electrode. © 2013 Pleiades Publishing, Ltd

Thermodynamic properties of uranium in Ga-In based alloys

Activity of uranium was determined in gallium, indium and gallium-indium eutectic (21.8 wt.% In) based alloys between 573 and 1073 K employing the electromotive force method. In two-phase U-Ga-In alloys, uranium forms the intermetallic compound UGa3. Activity coefficients and solubility of uranium in Ga-In eutectic were also determined in the same temperature range. Partial thermodynamic functions of γ-U in saturated alloys with gallium, indium and Ga-In eutectic were calculated. © 2013 Elsevier B.V. All rights reserved

Reduction of Tantalum Pentoxide with Aluminium and Calcium: Thermodynamic Modelling and Scale Skilled Tests

High reactivity of powdered aluminium together with its relatively low price are the main reasons for the application of this metal as a reducing agent for the reduction of oxides and fluorides of rare and rare earth metals by the aluminothermal method. This technology is widely used in the production of master alloys for ferrous metallurgy. The "out-of-furnace" process (i.e. without external heat access) is the prevailing technology for metallic niobium production worldwide. However, aluminothermal reduction for industrial production of metallic tantalum has been limited because of the high required temperature, over 2800 °C. In this paper the results of simultaneous reduction of tantalum(V) and iron(III) oxides by calcium-aluminothermal "out-of-furnace" process are presented. Powdered aluminium and metallic calcium were used as reductants. The pickup of tantalum at smeltings with the mass of raw materials over 1 kg reached 94%. The metal was obtained in the form of compact ingot; separation of metallic and slag phases was excellent. Crushed melt underwent refining remelting in an electron beam furnace. For thermodynamic studies and optimization of the aluminothermal reduction processes of Ta2O5 and Fe2O3 in the temperature range of 1000-3000°C a licensed computer simulation program "HSC Chemistry 6.1, 2007", elaborated by the company Outotec Oy, was applied