11 Life cycle model 资产组合PPT 金融系，研究生课程课件.pptVIP

Chapter 11Life-cycle Individual portfolio management with Background risk Preview Age and portfolio management Working hours and portfolio management Junior can’t borrow House and portfolio management Marriage and portfolio management Life style and LDI Vocation and portfolio management Bodie ：Comparison of Paradigms of Life-Cycle Finance  Old Paradigm New Paradigm Model Intuition and background the individual simultaneously determines optimal levels of current consumption, labor effort and leisure, and an optimal investment portfolio at each point in the life cycle. [关注如何花钱] disastrous portfolio performance will induce the individual to increase his labor supply Heterogeneous background of each investor Age Wealth Wage An illustration: 60% of total wealth is in risky asset Case 1 flexible and low volatile labor, induces high risky financial asset Case 2 fixed labor suuply, induces low risky financial asset Case 3 high volatile labor， lower risky financial asset BMS Model Assumption Bodie, Merton and Samuelson(1992) An individual lives from time 0 to T. He begins with financial wealth F(0). At any time t, his current financial wealth F(t) is determined by his past saving and investment decisions. he possesses wealth in the form of his human capital. This human capital H(t) embodies the present value of his future labor income. At each point in time, the individual may invest his financial wealth in one of two assets: a risk-free asset and risky asset, x(t) is the risky asset proportion. determines his rate of consumption C(t),. determines the quantity of labor ratio L(t) in each year, subject to L(t) + h(t) = 1. BMS Model I: When labor is flexible Target:J(W,w,t)= max Et[∫0Te-δs u(C(s), L(s))ds] ---（Continuous） Example: u(C, L)=log(C)+Гlog(L) Initial condition H(t)=ω(t)(1- e-(r-g)(T-t) )/(r-g) Constraints dW=[(x(α-r)+r)W-C- ω L]dt+σxWdz Solution W,w,t are state variables, C,L,X are control