Designing Novel Sulphate-based Ceramic Materials as Insertion Host Compounds for Secondary Batteries

Rechargeable batteries have propelled the wireless revolution and automobiles market over the past 25 years. Developing better batteries with improved energy density demands unveiling of new cathode ceramic materials with suitable diffusion channels and open framework structure. In this pursuit of achieving higher energy density, one approach is to realize enhanced redox voltage of insertion of ceramic compounds. This can be accomplished by incorporating highly electronegative anions in the cathode ceramics. Building on this idea, recently various sulphate- based compounds have been reported as high voltage cathode materials. The current article highlights the use of sulphate (SO4) based cathodes to realize the highest ever Fe3+/Fe2+ redox potentials in Li-ion batteries (LiFeSO4F fluorosulphate: 3.9V vs Li/Li+) and Na-ion batteries (Na2Fe2(SO4)(3) polysulphate: 3.8V vs Na/Na+). These sulphate-based cathode ceramic compounds pave way for newer avenues to design better batteries for future applications.

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.

The promise of fuel cell-based automobiles

Fuel cell-based automobiles have gained attention in the last few years due to growing public concern about urban air pollution and consequent environmental problems. From an analysis of the power and energy requirements of a modern car, it is estimated that a base sustainable power of ca. 50 kW supplemented with short bursts up to 80 kW will suffice in most driving requirements. The energy demand depends greatly on driving characteristics but under normal usage is expected to be 200 Wh/km. The advantages and disadvantages of candidate fuel-cell systems and various fuels are considered together with the issue of whether the fuel should be converted directly in the fuel cell or should be reformed to hydrogen onboard the vehicle. For fuel cell vehicles to compete successfully with conventional internal-combustion engine vehicles, it appears that direct conversion fuel cells using probably hydrogen, but possibly methanol, are the only realistic contenders for road transportation applications. Among the available fuel cell technologies, polymer-electrolyte fuel cells directly fueled with hydrogen appear to be the best option for powering fuel cell vehicles as there is every prospect that these will exceed the performance of the internal-combustion engine vehicles but for their first cost. A target cost of $ 50/kW would be mandatory to make polymer-electrolyte fuel cells competitive with the internal combustion engines and can only be achieved with design changes that would substantially reduce the quantity of materials used. At present, prominent car manufacturers are deploying important research and development efforts to develop fuel cell vehicles and are projecting to start production by 2005.

Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.