LINEBURG

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CSTVA, 19, 139, 141

big subintervals, 42â€“44, 101

boundary conditions, 6, 97

damped oscillator, 12, 39, 40, 54, 143

business cycle instabilities, 39

damping function, 89

DE solver, 15, 21, 22, 26

candidate selection systems, 13 decision variables, 13

cash management, 4 deterministic, 1, 4, 18

co-efficient, 7, 13 deterministic optimization, 2

co-state function, 6, 9, 15 difference of optimal control policy sequences,

computational algorithms, 1, 10, 14, 20, 21, 101 10

computational experiments, xvii, 36, 89 discount factor, 24

computational methods, 1, 11, 19, 24, 27, 40, discrete optimal control models, 10

97, 100, 101, 141 discretization augment, 18

CONMIN, 11 division of the time intervals, 10

constant-input arcs, 16 Dodgem problem, 12

constr, 15, 20, 25â€“28, 44, 45, 102, 141, 189 dynamic behavior, 40

continuous optimal control models, 10 dynamic equation, 7, 18, 23, 28, 29, 102, 189

dynamic financial system, 1, 39, 40, 142

control, 2, 12â€“14, 20, 22, 26, 27, 30, 31, 33, 36,

dynamic optimization models, 1, 3

37, 39â€“47, 54, 61, 67, 86, 88, 103â€“

dynamic programming, 10, 11

105, 111â€“113, 115â€“122, 142

control discretization approach, 10

control function, xvi, 9, 14, 18, 19, 21, 23, 39, economic models, 14, 15

142, 189 end-point constraint, 98

control mechanism, 89 end-points, 10, 42, 43

control parameterization knot points, 16

control parameterization technique, 11, 12 financial decision making, 3, 30, 39, 41

200 OPTIMAL CONTROL MODELS IN FINANCE

financial engineering, 4 multi-state functions, 40

financial market, 89, 92

necessary conditions, 6, 17, 96

financial optimal control models, 2, 8, 18, 22,

non-linear complex dynamic behavior, 89

139, 141â€“143

non-linear control system, 17

financial optimization models, 2, 4

non-linear transformation, 20, 21

financial planning, 4, 142

non-smooth functions, 12

financial sector, 39, 89

nqq computer package, 41

financial system, 1, 39â€“41, 43, 54, 88, 102, 111,

nqq function, 20

115, 139, 142

finite difference approximation, 15

obstacle, 18

finite difference method, 141

OCIM, 11, 12, 14, 18

finite horizon models, 4

ODE, 15, 19

Fish problem, 12

operations research, 2

fishery harvesting model, 12

optimal consumption, 4

fitting functional, 21, 30â€“33, 35, 48, 54, 109, 110,

optimal control modeling, 1, 142

113â€“115, 118â€“122, 139

optimal control problems, 1, 2, 4, 7, 8, 10â€“15,

fixed-time control, 3

17, 20, 23, 25

fixed-time optimal control problem, 11, 23, 25

optimal control theory, 1

fixed-time period, 19

optimal controller, 95

forcing function, 41, 114

optimal corporate finance, 4, 92

optimal investment planning, 4, 20, 36, 89, 141

global minimum, 5, 10, 18, 54, 116, 122

optimal investment strategy, 89

gradient search methods, 10, 11

optimal path, 18

grid-points, 11, 14, 19, 26, 29, 31, 45, 102

optimal portfolio choice, 4

optimization criteria, 3

Hamiltonian, 4, 6, 9, 15, 96

oscillator problem, 12, 36, 37, 40, 44â€“46, 120,

124, 142

implicit constraints, 14, 15

oscillatory behavior, 39

indifference principle, 8â€“10

oscillatory dynamics, 39, 89

infinite horizon models, 4

oscillatory financial model, 39

initial and terminal conditions, 4

inter-temporal time preference, 3

penalty constant, 13

interpolation, 11

penalty term, 14, 91, 98, 99, 142

investment, 4, 30, 36, 41, 89, 91â€“93, 102, 110,

piece-wise continuous function, 2

113, 141â€“143

piecewise-linear transformation, 20, 21, 25, 29,

investment allocation, 91, 143

141

investment model, 16

planning horizon, 2, 6, 31, 94, 98, 101

Pontryagin theorem, 2, 6, 8, 9, 18

Karush-Kuhn-Tucker, 5 Pontryaginâ€™s Maximum Principle, 17

Lagrange multipliers, 5, 98, 99 Quadratic Programming sub-problem, 25

Leap-Frog Algorithm, 17 quasi-Newton updating method, 11, 25

linear interpolation, 11, 15, 29, 46, 103, 187

local minimum, xvii, 4, 10, 116, 118, 122 real-world problems, 1, 2

low-pass filter, 11 restricted domain, 18

reverse-time construction technique, 94

mathematical programming, 4, 94 RIOTS, 11, 12, 18, 19

mathematical structure, 1, 4 risk management, 4

MATLAB, xvi, xvii, 11, 12, 14, 15, 18, 20, 25â€“

scaled time, 22, 28â€“30, 42, 43, 45â€“7, 100, 102,

28,44,45, 101, 102, 141, 189

Maximum Principle, 2, 4, 94, 96 103

maximum principle, 8â€“10 SCOM, 12, 21, 25

second order differential equation, 20, 39, 40,

minimization problem, 2, 4â€“6, 18, 27, 30, 44,

98, 102 45, 46, 141

sequential quadratic programming method, SQP,

MISER, 11, 12, 14, 17â€“19

20, 25, 141

mixed discrete and continuous optimal control

single-input non-linear system, 16

problem, 13

INDEX 201

singular arc, 7, 16, 26, 41, 97 system parameters, 13, 44

stabilization mechanism, 39

stable optimal investment planning, 89 terminal constraint transformation, 98

state variables, 93, 97, 111

terminal manifold, 94

STC, 16, 17, 19

time optimal control problems, 16

step function, 3, 10, 11, 14, 15, 18â€“21, 25, 26,

time scale, 23, 39, 41, 42, 99

40, 120, 141, 142, 189

time subdivision, 40, 108

stochastic, 1, 4, 16, 18

time transformation, 21, 101

stochastic finance, 4

time-optimal control, 3

stochastic financial optimal control model, 18

time-optimal control problems, 23

STV algorithm, 19, 20, 141, 143

TOBC, 17

switching control, 3, 27, 41, 86, 89

TPBVP, 17

switching time computation method, 16

two-point boundary-value problem, 17

switching time variable method, 141

switching times, 13, 17, 19, 26, 27, 29, 31, 32,

35, 36, 39, 43, 46, 47, 67, 89 valuation, 4

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