In its simplest expression, the existence of a riskless asset
in sufficient large supply will determine [r.sub.t+1].
The financial market under consideration consists of n risky assets with random returns and one riskless asset
with a deterministic return.
where [R.sup.f(1).sub.t+j] denotes the one-period net return on a riskless asset
and [Rf.sup.e(1).sub.t+j] denotes a vector of one-period excess returns above the riskless return for the number of risky assets under consideration.
* R is the low risk return rate: it is the return rate of a riskless asset
whose emitter is characterized by a higher level of solvency (example, Sovereign Sukuk Ijara (8)).
where [[theta].sub.S](t), [[theta].sub.L] (t), and [[theta].sub.r] (t) denote the amounts of capital invested in the two risky assets (security and loan) and in the riskless asset
For long-horizon investors, long-term inflation-indexed bonds are the riskless asset
. By investing in a portfolio of inflation-indexed bonds whose cash flows match their consumption spending plans, investors can guarantee a riskless consumption stream.
Another riskless asset
is a loan to a sovereign government.
Let us assume that for a given time t the agent can allocate his wealth among n - 1 risky assets with a stochastic rate of return [r.sub.it] and a riskless asset
with a rate of return [r.sub.0t].
Kingston (2000) and Farhi and Panageas (2007) study the optimal retirement timing decision combined with the problem of optimal sav- ing and asset allocation prior to retirement, where available assets are one risky and one riskless asset
, as in Merton (1971).
And bond [B.sub.t] with riskless interest rate r [[theta].sup.0.sup.t] and [[theta].sup.1.sub.t] represents the position of risk asset and riskless asset
held in the portfolio, then the wealth process V = [[theta].sup.0.sub.t][B.sub.t] + [[theta].sup.0.sub.t][S.sub.t].
We consider a financial market [M.sup.n+1] which consist of a riskless asset
and n risky assets, traded upon continuously.