Liquidity constraints and asset allocation: a model for the insurance firm.

Author:Said, Hassan A.

    Financial firms in general and insurers in particular face various business uncertainties. Among these is the choice between the degree of liquidity of their assets and their profitability. The degree of liquidity of an asset is defined here as its ability to convert to cash without undue time or undue loss. Models balancing the profitability and riskiness of financial assets of the financial firms are shown to be useful for the analysis of the firm's solvency (Pyle, 1971, and Kahane, Tapiero, and Jacques, 1989). Liabilities (claims) and investment processes induce several types of costs in terms of which solvencies are defined. For the purpose of this research the solvency is defined in terms of the company's liquidity. The firm is considered solvent as long as it is able to meet its current obligations as they fall due. To overcome the problem of temporary illiquidity, generally a firm may be able to borrow in the open market; so long the firm's assets exceed its liabilities in the long-term sense. For a long time, banking executives and insurance actuaries have discussed their risk planning and reinsurance agreements, often with the explicit purpose of reducing the fluctuations in the company's operational risks and underwriting results, but have only occasionally indicated that these fluctuations may be accentuated by fluctuations in the company's investment results. Given the duration and the nature of the insurance firm liability-contracts, liquidity position is thought to depend on both underwriting and investment activities, rather than on investment or underwriting separately. Muller (1985) shows that a typical pension fund firm, with long-term contracts, faces two types of risk: actuarial risk and investment risk. His attempt dealt with unifying both risks to derive optimal solution. He finds an inverse relationship between the fraction of reinsurance and the expected rate of return on investment, and that the size of the fund is independent of the optimal investment policy. The proposed simplified model is based on the proposition that an overall company performance is a function of liquidity needs for claim payments, given its underwriting capacity and the reinsurance arrangements. It is also dependent on the company's investment returns, given the size of its capital. The model incorporates the liquidity concerns of investment and underwriting results to yield a stochastic model of assets allocation.

    The paper examines a class of analytic problems arising from an interesting stochastic allocation process, usually occurring in the study of management science, more specifically in inventory theory and stock control. The problem is a very particular case of a more general problem of decision-making in the face of an uncertain demand. The study of inventory control dates back to the work of Arrow, Harris and Marshcak, 1951, and Bellman, 1957. A typical firm seeks to determine the optimal inventory level when demand is known only stochastically. The version considered here is similar to the problem of stocking a supply of items to meet an uncertain demand, under the assumptions that there are various costs associated with, for example, under-supply (unfulfilled demand). In the financial sector, a company must balance its carrying costs of holding cash and other forms of assets against losses it may suffer should it be unable to meet liquidity needs for demand of its customers. Analogously, the cash management problem considers the dilemma faced by companies when they must decide about the appropriate level of inventory (cash) to keep on hand. Since demand for cash fluctuates, a manager can decide to raise cash via liquidation of current investments and borrow in the open market, or reduce cash by increasing investment level, in hopes of matching the on hand cash with the uncertain demand. In either case, holding large amounts of cash on hand results in lost opportunity (lower return on investments), while shortage of cash results in additional costs of borrowing that may lead to added burden on profitability or delays in meeting current obligations (facing the risk of insolvency). Building on the same theme the company should balance its stochastic requirement of funds for both assets investments and liabilities payments to maximize profit.


    Generally the liabilities of a financial firm consist of a portfolio of contracts (e.g., policy reserves, deposits). For an insurance company, the liabilities are...

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