P

Markov chain transition matrix

(ω+a)×(ω+a)

U

Survival and age transition matrix

ω×ω

M

Mortality matrix

a×ω

R
_{
i
}

Matrix of ith moments of rewards

(ω+a)×(ω+a)

ρ
_{
i
}

Vector of ith moments of lifetime accumulated reward

(ω+a)×1

\(\tilde {\boldsymbol {\rho }}_{i}\)

As ρ_{
i
}, but for living states

ω×1

Z

01 matrix to select living states

ω×(ω+a)

N

Fundamental matrix

ω×ω

η
_{1}

Vector of ith moments of remaining longevity

ω×1

ω

Number of age classes

scalar

a

Number of absorbing (dead) states

scalar
