LINEBURG


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bang-bang optimal control solution, 40
CSTVA, 19, 139, 141
big subintervals, 42“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, 25“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, 12“14, 20, 22, 26, 27, 30, 31, 33, 36,
dynamic optimization models, 1, 3
37, 39“47, 54, 61, 67, 86, 88, 103“
dynamic programming, 10, 11
105, 111“113, 115“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, 141“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, 39“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, 30“33, 35, 48, 54, 109, 110,
optimal control modeling, 1, 142
113“115, 118“122, 139
optimal control problems, 1, 2, 4, 7, 8, 10“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, 44“46, 120,
124, 142
implicit constraints, 14, 15
oscillatory behavior, 39
indifference principle, 8“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, 91“93, 102, 110,
piece-wise continuous function, 2
113, 141“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 Pontryagin™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, 25“
scaled time, 22, 28“30, 42, 43, 45“7, 100, 102,
28,44,45, 101, 102, 141, 189
Maximum Principle, 2, 4, 94, 96 103
maximum principle, 8“10 SCOM, 12, 21, 25
second order differential equation, 20, 39, 40,
minimization problem, 2, 4“6, 18, 27, 30, 44,
98, 102 45, 46, 141
sequential quadratic programming method, SQP,
MISER, 11, 12, 14, 17“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, 18“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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