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.

Trends in consanguineous marriage in Karnataka, South India, 1980–89

Analysis of data on 106,848 marriages in the cities of Bangalore and Mysore, South India, between 1980 and 1989 showed that levels of consanguineous marriage varied between cities through time and by religion. The average coefficient of inbreeding was higher in Bangalore (F = 0·0339) than in Mysore (F = 0·0203), principally reflecting large-scale, post-Independence rural migration into Bangalore. Although there was some evidence of a decline in consanguineous marriages in Mysore, there was no convincing support in either city for earlier projections of a rapid reduction in the popularity of unions between close biological relatives.

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.

Molecular Marriage through Partner Preferences in Covalent Cage Formation and Cage-to-Cage Transformation

Unprecedented self-sorting of three-dimensional purely organic cages driven by dynamic covalent bonds is described. Four different cages were first synthesized by condensation of two triamines and two dialdehydes separately. When a mixture of all the components was allowed to react, only two cages were formed, which suggests a high-fidelity self-recognition. The issue of the preference of one triamine for a particular dialdehyde was further probed by transforming a non-preferred combination to either of the two preferred combinations by reacting it with the appropriate triamine or dialdehyde.

Hydrogen-Bond-Driven Controlled Molecular Marriage in Covalent Cages

A supramolecular approach that uses hydrogen-bonding interaction as a driving force to accomplish exceptional self-sorting in the formation of imine-based covalent organic cages is discussed. Utilizing the dynamic covalent chemistry approach from three geometrically similar dialdehydes (A, B, and D) and the flexible triamine tris(2-aminoethyl)amine (X), three new 3+2] self-assembled nanoscopic organic cages have been synthesized and fully characterized by various techniques. When a complex mixture of the dialdehydes and triamine X was subjected to reaction, it was found that only dialdehyde B (which has OH groups for H-bonding) reacted to form the corresponding cage B3X2 selectively. Surprisingly, the same reaction in the absence of aldehyde B yielded a mixture of products. Theoretical and experimental investigations are in complete agreement that the presence of the hydroxyl moiety adjacent to the aldehyde functionality in B is responsible for the selective formation of cage B3X2 from a complex reaction mixture. This spectacular selection was further analyzed by transforming a nonpreferred (non-hydroxy) cage into a preferred (hydroxy) cage B3X2 by treating the former with aldehyde B. The role of the H-bond in partner selection in a mixture of two dialdehydes and two amines has also been established. Moreover, an example of unconventional imine bond metathesis in organic cage-to-cage transformation is reported.

Sunlight-Induced Covalent Marriage of Two Triply Interlocked Pd-6 Cages and Their Facile Thermal Separation

A template-free triply interlocked Pd-6 cage (2) was synthesized by two-component self-assembly of cis-blocked 90 degrees acceptor cis-(tmen)Pd(NO3)(2) (M) and 1,3,5-tris((E)-2-(pyridin-3-yl)vinyl)benzene (L). Assembly 2 was characterized by H-1 NMR and ESI-MS, and the structure was confirmed by X-ray crystallography, which revealed a parallel conformation of the olefin double bonds belonging to the adjacent cages in the solid state at a distance of 3.656 angstrom, thereby indicating the feasibility of 2+2] photochemical reaction. Two adjacent interlocked cages were covalently married together by intermolecular 2+2] cycloaddition in a single crystal-to-single crystal fashion upon exposure to sunlight/UV irradiation. Most surprisingly, the covalently married pair was easily separated thermally in aqueous medium under mild reaction conditions.