Optimal consumption and portfolio choice with ambiguous interest rates and volatility
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Optimal consumption and portfolio choice with ambiguous interest rates and volatility Qian Lin1 · Frank Riedel2,3 Received: 5 February 2020 / Accepted: 24 August 2020 © The Author(s) 2020
Abstract We study continuous-time consumption and portfolio choice in the presence of Knightian uncertainty about interest rates. We develop the stochastic model that involves singular priors and analyze optimal behavior. When there is sufficiently large uncertainty about interest rates, the agent invests in the asset market only and abstains from the bond market. Keywords Portfolio Choice · Knightian Uncertainty · Model uncertainty · Interest Rate Ambiguity JEL Classification D81 · G11 · G12
1 Introduction Optimal consumption and portfolio decisions play a fundamental role for individual investors, pension funds, and insurance companies alike. Life-cycle models also form the basic building block for more complex economic models that are used in economic policy and governance discussions. In this paper, we consider an otherwise standard
This work is supported by the National Natural Science Foundation of China (No. 11971364), and the German Research Foundation (DFG) via Grant Ri-1128-7-1 and the CRC 1283.
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Frank Riedel [email protected] Qian Lin [email protected]
1
School of Economics and Management, Wuhan University, Wuhan, China
2
Center for Mathematical Economics, Bielefeld University, Bielefeld, Germany
3
Department of Economic and Financial Sciences, University of Johannesburg, Johannesburg, South Africa
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Q. Lin, F. Riedel
life-cycle consumption and portfolio problem for an investor who faces Knightian uncertainty about interest rates.1 Interest rates vary considerably over time. Equilibrium interest rates depend on the economy’s growth, the volatility of the market, and agents’ preference parameters as subjective discount rate, risk aversion, and intertemporal rate of substitution. All these parameters are hard to predict or estimate in the long run. While investors were used to high levels of interest rates in the 1970s when the treasury rate in the US, e.g., fluctuated around 10%, we have by now an extended period of very low interest rates around the zero level. The level of interest rates is strongly influenced by central bank policies. Last not least, inflation adds an additional flavor of uncertainty that is difficult to model or predict. For a long term investor, there is thus no riskless asset. While the consumption and portfolio choice problem for investors who face Knightian uncertainty about the returns of risky assets has been amply studied (see below), the role of Knightian or model uncertainty of interest rates has not been tackled so far. We thus develop here a model that allows to discuss the impact of interest rate uncertainty on optimal investment and consumption decisions within the classic Samuelson continuous-time life cycle model. We take model uncertainty about the short rate and, in fact, the whole term structure, into account. We consider an investor who is willing to
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