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.

Ultracapacitor Based Ride Through System for Control Power Supplies in High Power Converters

High power converters are used in variable speed induction motor drive applications. Riding through a short term power supply glitch is becoming an important requirement in these power converters. The power converter uses a large number of control circuit boards for its operation. The control power supply need to ensure that any glitch in the grid side does not affect any of these control circuit boards. A power supply failure of these control cards results in shut down of the entire system. The paper discusses the ride through system developed to overcome voltage sags and short duration outages at the power supply terminals of the control cards in these converters. A 240VA non-isolated, bi-directional buck-boost converter has been designed to be used along with a stack of ultracapacitors to achieve the same. A micro-controller based digital control platform made use of to achieve the control objective. The design of the ultracapacitor stack and the bidirectional converter is described the performance of the experimental set-up is evaluated.

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.

Beat frequency oscillations in the output voltage of high voltage DC power supplies under pulsed loading

High voltage power supplies for radar applications are investigated, which are subjected to pulsed load (125 kHz and 10% duty cycle) with stringent specifications (<0.01% regulation, efficiency>85%, droop<0.5 V/micro-sec.). As good regulation and stable operation requires the converter to be switched at much higher frequency than the pulse load frequency, transformer poses serious problems of insulation failure and higher losses. Few converter topologies are proposed to tackle these problems. A study is made regarding the beat frequency oscillations that may exist with pulsed loading. It is illustrated with respect to the proposed converter topologies. Methods are proposed to eliminate or minimize these oscillations.

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.

Cyclodextrin-functionalized Fe3O4@TiO2: reusable, magnetic nanoparticles for photocatalytic degradation of endocrine-disrupting chemicals in water supplies

Water-dispersible, photocatalytic Fe3O4@TiO2 core shell magnetic nanoparticles have been prepared by anchoring cyclodextrin cavities to the TiO2 shell, and their ability to capture and photocatalytically destroy endocrine-disrupting chemicals, bisphenol A and dibutyl phthalate, present in water, has been demonstrated. The functionalized nanoparticles can be magnetically separated from the dispersion after photocatalysis and hence reused. Each component of the cyclodextrin-functionalized Fe3O4@TiO2 core shell nanoparticle has a crucial role in its functioning. The tethered cyclodextrins are responsible for the aqueous dispersibility of the nanoparticles and their hydrophobic cavities for the capture of the organic pollutants that may be present in water samples. The amorphous TiO2 shell is the photocatalyst for the degradation and mineralization of the organics, bisphenol A and dibutyl phthalate, under UV illumination, and the magnetism associated with the 9 nm crystalline Fe3O4 core allows for the magnetic separation from the dispersion once photocatalytic degradation is complete. An attractive feature of these ``capture and destroy'' nanomaterials is that they may be completely removed from the dispersion and reused with little or no loss of catalytic activity.

Design Of Start-up Power Circuit For Control Power Supplies With Wide Input Voltage Variation

This paper presents the design of a start up power circuit for a control power supply (CPS) which feeds power to the sub-systems of High Power Converters (HPC). The sub-systems such as gate drive card, annunciation card, protection and delay card etc; needs to be provided power for the operation of a HPC. The control power supply (CPS) is designed to operate over a wide range of input voltage from 90Vac to 270Vac. The CPS output supplies power at a desired voltage of Vout =24V to the auxiliary sub-systems of the HPC. During the starting, the power supply to the control circuitry of CPS in turn, is obtained using a separate start-up power supply. This paper discusses the various design issues of the start-up power circuit to ensure that start-up and shut down of the CPS occurs reliably. The CPS also maintains the power factor close to unity and low total harmonic distortion in input current. The paper also provides design details of gate drive circuits employed for the CPS as well as the design of on-board power supply for the CPS. Index terms: control power supply, start-up power supply, DSFC, pre-regulator