Practical Finance Strategies in Immunization

Abstract

My first goal is to present the basic immunization problem (BIP) as it is understood in finance. BIP relies on a construction of such a bond portfolio (BP), meaning a selection of individual bonds, that the single liability to pay L dollars q years from now will be discharged by means of BP (a patient will return to health at time q), no matter what random shift a(t) (a particular disease) will occur in the future. What kind of a function is a shift of interest rates is critically important because both present and future values of BP depend solely on underlying interest rates. Having identified shifts (diseases) against which a BP is immunized, the natural question arises how to find among such immunized (immune) portfolios the best ones. In the context of finance, it means bond portfolios with maximal unanticipated rate of return. My second goal is to trigger interest among medical scientists by suggesting that certain finance notions, such as duration and convexity of a bond portfolio, might give extra insight to medical researchers working in the immunization area both into BIP and into similar problems in medicine. A considerable attention is also paid to certain mathematical notions (base of a linear space, a Hilbert space, triangular functions) because of their successful applications to problem-solving occurring in bond portfolio immunization.